SAS Econometrics and Time Series Analysis 2 for JMP. Third Edition

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1 SAS Econometrics and Time Series Analysis 2 for JMP Third Edition

2 The correct bibliographic citation for this manual is as follows: SAS Institute Inc SAS Econometrics and Time Series Analysis 2 for JMP, Third Edition. Cary, NC: SAS Institute Inc. SAS Econometrics and Time Series Analysis 2 for JMP, Third Edition Copyright 2013, SAS Institute Inc., Cary, NC, USA ISBN All rights reserved. Produced in the United States of America. For a hard-copy book: No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, or otherwise, without the prior written permission of the publisher, SAS Institute Inc. For a web download or e-book: Your use of this publication shall be governed by the terms established by the vendor at the time you acquire this publication. The scanning, uploading, and distribution of this book via the Internet or any other means without the permission of the publisher is illegal and punishable by law. Please purchase only authorized electronic editions and do not participate in or encourage electronic piracy of copyrighted materials. Your support of others rights is appreciated. U.S. Government Restricted Rights Notice: Use, duplication, or disclosure of this software and related documentation by the U.S. government is subject to the Agreement with SAS Institute and the restrictions set forth in FAR , Commercial Computer Software Restricted Rights (June 1987). SAS Institute Inc., SAS Campus Drive, Cary, North Carolina June 2013 SAS provides a complete selection of books and electronic products to help customers use SAS software to its fullest potential. For more information about our e-books, e-learning products, CDs, and hard-copy books, visit support.sas.com/bookstore or call SAS and all other SAS Institute Inc. product or service names are registered trademarks or trademarks of SAS Institute Inc. in the USA and other countries. indicates USA registration. Other brand and product names are registered trademarks or trademarks of their respective companies.

3 Contents Credits v Chapter 1. About This Book Chapter 2. Introduction to SAS Econometrics and Time Series Analysis for JMP Chapter 3. Getting Started with SAS Econometrics and Time Series Analysis for JMP Chapter 4. Fit Y by X with Autocorrelated and Heteroscedastic Errors Chapter 5. Fit Count Data Regression Chapter 6. Fit Panel Data Regression Chapter 7. Model Severity of an Event Chapter 8. Fit Instrumental Variables Regression Chapter 9. Fit Unobserved Components Models

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5 Credits Documentation Writing Editing Documentation Support Ruth Baldasaro, June Ge, Qingsong Yang Anne Baxter Tim Arnold, Sharad Prabhu Software SAS Econometrics and Time Series Analysis for JMP Interface Design Jan Chvosta, Mark Little, Sharad Prabhu Interface Coding Joseph Morgan, Sharad Prabhu, Qingsong Yang SAS/ETS Procedures PROC AUTOREG PROC COUNTREG PROC PANEL PROC SEVERITY PROC SYSLIN PROC UCM Xilong Chen, Jan Chvosta, Richard Potter, Jason Qiao, John P. Sall Jan Chvosta, Laura Jackson Jan Chvosta, Greg Sterijevski Mahesh V. Josh Laura Jackson, Donald J. Erdman, Leigh A. Ihnen, John P. Sall Rajesh Selukar

6 Support Groups Software Testing Technical Support John Crouch Duane Hayes vi

7 Chapter 1 About This Book This book describes the features of SAS Econometrics and Time Series Analysis for JMP and includes instructions for performing analyses. This book does not contain a comprehensive treatment of econometric and time series analyses or more technical details regarding the SAS/ETS procedures. For more information about econometric and time series analyses, see Greene (2000). For more information about the SAS/ETS procedures, see the SAS/ETS User s Guide. This book is organized as follows: This chapter describes the organization of the book. Chapter 2 provides a brief description of SAS Econometrics and Time Series Analysis for JMP. Chapter 3 gets you started with a simple example of how to use SAS Econometrics and Time Series Analysis for JMP. Chapter 4 provides an overview of how to perform a Fit Y by X with Autocorrelated and Heteroscedastic Errors analysis, a detailed description of the available features, and a comparison to the JMP Time Series platform. Chapter 5 provides an overview of how to perform a Fit Count Data Regression analysis, a detailed description of the available features, and several plots and a frequency report that are available for analyzing count data. Chapter 6 provides an overview of how to perform a Fit Panel Data Regression analysis and a detailed description of the available features. Chapter 7 provides an overview of how to perform a Model Severity of an Event analysis, a detailed description of the available features, and several plots that are available for analyzing severity data. Chapter 8 provides an overview of how to perform a Fit Instrumental Variables Regression analysis and a detailed description of the available features. Chapter 9 provides an overview of how to perform a Fit Unobserved Components Models analysis and a detailed description of the available features. References Greene, W. H. (2000), Econometric Analysis, 4th Edition, Upper Saddle River, NJ: Prentice-Hall.

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9 Chapter 2 Introduction to SAS Econometrics and Time Series Analysis for JMP Contents Overview Specify an Analysis Initial Model Window Results Window Data Summary Area Fitted Models Area Model Comparison Area Model Estimates Area Dialog Window Add-in Main Menu SAS Graphs Settings Window Display Settings Window Overview SAS Econometrics and Time Series Analysis for JMP is a graphical user interface that provides easy access to SAS/ETS procedures. You can specify a model in JMP, and SAS Econometrics and Time Series Analysis for JMP uses the relevant SAS/ETS procedures for model estimation. The results from the SAS/ETS procedures are returned to JMP and displayed in a JMP window. SAS Econometrics and Time Series Analysis for JMP provides the following analyses: Fitting Y by X with autocorrelated and heteroscedastic errors enables you to fit models to time series data when the errors are autocorrelated or heteroscedastic. Fitting count data regression enables you to perform count analysis when the dependent variable takes nonnegative integer or count values. Fitting panel data regression enables you to perform panel analysis when you have both time series and cross-sectional data. Modeling severity of an event enables you to model the magnitude (severity) of a continuous-valued event of interest. Fitting instrumental variables regression enables you to fit model that has endogenous regressors.

10 4 Chapter 2: Introduction to SAS Econometrics and Time Series Analysis for JMP Fitting unobserved components models enables you to fit unobserved components models to equally spaced univariate time series data. Each analysis has a similar structure with four types of windows: initial model, results, options, and settings windows. This chapter contains an overview of each of these window types. The subsequent chapters provide detailed descriptions of these windows and instructions for how to specify each analysis. You can access SAS Econometrics and Time Series Analysis for JMP by selecting SAS I Econometrics and Time Series from the JMP Home window. The Econometrics and Time Series menu contains six analysis commands, ETS sample data, and the help documentation. The analysis commands are described in detail in Chapter 4, Chapter 5, Chapter 6, Chapter 7, Chapter 8, and Chapter 9. Specify an Analysis Creating an analysis consists of the following basic steps (step 1 through 3 for each analysis type are described in detail in Chapter 4, Chapter 5, Chapter 6, Chapter 7, Chapter 8, and Chapter 9): 1 In the initial model window, specify and estimate a base model. 2 In the results window, examine the base model results. 3 In the dialog window, create and estimate an alternative model. 4 In the results window, examine the results of the alternative model and compare the model to the base model. 5 Continue creating alternative models and comparing them with previous models until you are satisfied with the model fit. Initial Model Window The initial model window appears when you select an analysis from the Econometrics and Time Series menu. In this window, you specify the roles for the variables you want in the base model, which represents default parameter selections. You can change the base model later. The name of the initial model window and the options it contains depend on which analysis you select. See Chapter 4, Chapter 5, Chapter 6, Chapter 7, Chapter 8, and Chapter 9 for the name of and the options in the initial model window for each type of analysis. All of the initial model windows also have the following buttons: Click Cancel to close the window without saving the roles. Click Remove to remove highlighted roles. Click Recall to restore the saved roles that were selected in the most recently used model.

11 Results Window 5 Click Help to open the help manual. Figure 2.1 shows an example of the initial model window for Fit Y by X with Autocorrelated and Heteroscedastic Errors. Figure 2.1 Example Initial Model Window Results Window The results window contains plots and tables of results for the models you fit. The name of the results window depends on which analysis option is selected. Each results window contains four areas: Data Summary Fitted Models Model Comparison Model Estimates Each of these areas is described in detail in the following sections.

6 Chapter 2: Introduction to SAS Econometrics and Time Series Analysis for JMP Data Summary Area The Data Summary area includes plots and tables which depend on the selected analysis.

12 6 Chapter 2: Introduction to SAS Econometrics and Time Series Analysis for JMP Data Summary Area The Data Summary area includes plots and tables which depend on the selected analysis. An example of the Data Summary area for Fit Y by X with Autocorrelated and Heteroscedastic Errors is shown in Figure 2.2. Figure 2.2 Example Data Summary Area in the Results Window Fitted Models Area The Fitted Models area contains a list of the models that have been estimated. For each model, the list has a model name, a check box for including the model in the Model Comparison area, model fit statistics, and a description of the model. Click a model name to view the parameter estimates in the Model Estimates

Fitted Models Area 7 area. Click the column names to sort the models. For example, click a fit statistic title such as AIC (Akaike s information criterion) to sort the models by model fit values.

3 Example Results Window with Fitted Models Area The Fitted Models area has two types of red triangle menus: one type is next to the Fitted Models heading, and the other type is next to each model s

13 Fitted Models Area 7 area. Click the column names to sort the models. For example, click a fit statistic title such as AIC (Akaike s information criterion) to sort the models by model fit values. Figure 2.3 shows an example of the Fitted Models area for Fit Y by X with Autocorrelated and Heteroscedastic Errors. Figure 2.3 Example Results Window with Fitted Models Area The Fitted Models area has two types of red triangle menus: one type is next to the Fitted Models heading, and the other type is next to each model s name. Fitted Models Red Triangle Menu Figure 2.4 shows the fitted models red triangle menu next to the Fitted Models heading for all Results windows. The following commands are available in this menu: Figure 2.4 Fitted Models Red Triangle Menu New Model opens a dialog window. See the section Dialog Window on page 10 for more information. NOTE: This command is equivalent in functionality as the New Model button shown in the bottom of Fitted Models area (see Figure 2.3). Rerun all reruns all of the models. When the model properties in the Settings windows are changed, the changes are not implemented immediately. Select Rerun all to implement any changes to the settings for all models. NOTE: It takes longer to rerun all of the models if there are several models to rerun. Model Settings, SAS Graphics Settings, or Display Settings opens the Settings window. See the section Add-in Main Menu on page 11 for more information.

8 Chapter 2: Introduction to SAS Econometrics and Time Series Analysis for JMP Model Name Red Triangle Menu Figure 2.5 shows the red triangle menu that is next to each model name.

14 8 Chapter 2: Introduction to SAS Econometrics and Time Series Analysis for JMP Model Name Red Triangle Menu Figure 2.5 shows the red triangle menu that is next to each model name. The following commands are available in this menu: Edit opens a dialog window with the current model s settings. Delete deletes the model. Rename renames the model. Copy copies the model. Rerun reruns the model. View SAS Log opens a window with the SAS Log for the model. View/edit SAS code opens a SAS Program Editor window with the SAS code for the model. You can edit the SAS code for the model in this window. Figure 2.5 Model Name Red Triangle Menu Model Comparison Area The Model Comparison area is closed by default. To open this area, select one or more of the Compare boxes next to the model names in the Fitted Models area. The content shown in this area depends on the type of analysis. Figure 2.6 shows an example of the Model Comparison area for Fit Y by X with Autocorrelated and Heteroscedastic Errors. If only one model is selected, the original data and the fitted data are plotted in an overlay plot for comparison and a plot of the residuals is provided. If several models are selected, the fitted data for each model are plotted in one overlay plot with a different color for each model for both the fitted values and residuals plots.

15 Figure 2.6 Example Model Comparison Area in the Results Window Model Comparison Area 9

10 Chapter 2: Introduction to SAS Econometrics and Time Series Analysis for JMP Model Estimates Area The Model Estimates area displays the results generated by the SAS/ETS procedure for the current

16 10 Chapter 2: Introduction to SAS Econometrics and Time Series Analysis for JMP Model Estimates Area The Model Estimates area displays the results generated by the SAS/ETS procedure for the current model. Figure 2.7 shows an example of the Model Estimates area. Figure 2.7 Example Model Estimates Area in the Results Window Dialog Window When you create a new model or edit an existing model, you specify the model in the dialog window. When you create a new model, the window starts with default values; when you edit an existing model, the saved values of the current model appear in the window. The dialog windows are different for each analysis. See the following sections for more information: Autoregressive Error Regression Model Options Window on page 37 Count Data Analysis Options Window on page 53 Panel Data Regression Options Window on page 68

SAS Graphs Settings Window 11 Severity Data Analysis Options Window on page 81 Instrumental Variables Regression Options Window on page 98 The Unobserved Components Model Options Window on page 109

17 SAS Graphs Settings Window 11 Severity Data Analysis Options Window on page 81 Instrumental Variables Regression Options Window on page 98 The Unobserved Components Model Options Window on page 109 Add-in Main Menu Figure 2.8 shows the add-in red triangle menu in the upper left corner of the results window. The following commands are available in this menu: Model Settings opens a dialog window that saves preferences about add-in specific model settings. This is not available for all analyses. SAS Graphics Settings opens a dialog window that saves preferences about SAS graphics settings. This is not available for all analyses. Display Settings opens a dialog window that saves preferences about results display settings. This is available for all analyses. Save Analysis saves the analysis at its current state to a JMP project file. This is available for all analyses. The model, SAS graphics, and display settings are saved locally. When the settings are changed, the changes remain until you specify other settings. All analyses have a Display Settings window. Some analyses provide additional model settings windows. (See the sections Model Settings Window on page 42 and Forecast Settings Window on page 119.) Figure 2.8 Add-in Main Menu SAS Graphs Settings Window In the SAS Graphs Settings window, you specify which SAS graphs you want to be created. Figure 2.9 shows an example of the SAS Graphs Settings window. You can select paneled or individual plots. You can also select to plot none, all, or only recommended SAS ODS plots. The generated SAS ODS plots are displayed in the Model Estimates Area (see the section Model Estimates Area on page 10). NOTE: Generating all SAS graphs might take longer.

you specify the layout of the Model Comparison and Model Estimates areas of the Results

18 12 Chapter 2: Introduction to SAS Econometrics and Time Series Analysis for JMP Figure 2.9 SAS Graphics Settings Window Display Settings Window In the Display Settings window, you specify the layout of the Model Comparison and Model Estimates areas of the Results window. Figure 2.10 shows the Display Settings window. Figure 2.10 Display Settings Window

19 Chapter 3 Getting Started with SAS Econometrics and Time Series Analysis for JMP Contents Overview of Getting Started Example Data Description Example Models Description Perform an Analysis with SAS Econometrics and Time Series Analysis for JMP Establish a Connection to SAS Open the Data Set Create and Estimate the Base Model Examine the Base Model Results Create an Alternative Model Compare the Base and Alternative Models Save and Open the Results Save Results Open Results References Overview of Getting Started Example This getting started example shows you how to create and perform a panel data analysis in SAS Econometrics and Time Series Analysis for JMP. This example begins with a description of the data and the example models; then it shows you the steps for performing an analysis, including how to establish a connection to SAS, open a data set, create the panel data analysis base model, analyze the model, view the results, create an alternative model, and compare the models. This example also shows you how to save the analysis and open the results later. This example does not describe all the models you can create or all of the features of SAS Econometrics and Time Series Analysis for JMP. Throughout this example are directions about where to find more information about other features of SAS Econometrics and Time Series Analysis for JMP.

20 14 Chapter 3: Getting Started with SAS Econometrics and Time Series Analysis for JMP Data Description This example uses the airline data set, which is the frequently cited Christenson Associates airline data (Greene 2000). The data measure costs, prices of inputs, and utilization rates for six airlines over the 15 years (the observations span ). The variables include: I: firm ID T: time period ID C: total cost, in thousands Q: output in revenue passenger miles (index) PF: fuel price LF: load factor (utilization index) lc: log transformation of costs lq: log transformation of quantity lpf: log transformation of price of fuel Figure 3.1 shows part of the data set.

21 Example Models Description 15 Figure 3.1 Getting Started Example: Airline Data Example Models Description For this example, you create two models using Fit Panel Data Regression: a base model and an alternative model. Both models have LF, lq, and lpf as explanatory variables and lc as the response variable. The base model is a two-way fixed-effects model, which is the default model for Fit Panel Data Regression. The alternative model is a one-way, cross-sectional fixed-effects model, which ignores any time effects. One goal of this analysis is to determine which model is a better representation of the data. More specifically, does a model that includes a fixed effect of time fit better than a model that ignores time? A second goal is to determine how the explanatory variables are related to cost and which variables are significant predictors of cost.

22 16 Chapter 3: Getting Started with SAS Econometrics and Time Series Analysis for JMP Perform an Analysis with SAS Econometrics and Time Series Analysis for JMP Establish a Connection to SAS To use SAS Econometrics and Time Series Analysis for JMP, you need access to the SAS/ETS software. To create a connection to the SAS System: 1 Open JMP or later. 2 Select File I SASI Server Connection or SAS I Connect to SASI Server Connection. The SAS Server Connections window appears. 3 In the SAS Server Connections window, connect to the SAS System as described in one of the following subsections and then click Close to close the SAS Server Connections window. Connect to SAS on This Machine 1 Select Connect to SAS on this machine in the Establish New Workspace Server Connection area. 2 Click Connect. When the Open Workspace Server Connections area displays Current active connection: Local, you are connected to the SAS System. Connect to a SAS Metadata Server 1 Click Manage Profiles... in the Metadata Server Connection area. The Manage Metadata Server Profiles window appears. 2 Specify the appropriate metadata server information in the Manage Metadata Server Profiles window. 3 Click Connect to connect to the SAS Metadata server. When the Status displays Connected, you are connected to the SAS Metadata Server. 4 Click Close to close the Manage Metadata Server Profiles window. 5 Verify that the Connect to metadata-defined SAS server option is selected in the Establish New Workspace Server Connection area. 6 Click Connect. When the Open Workspace Server Connections area displays Current active connection followed by the name of the metadata server, you are connected to the SAS System.

23 Open the Data Set 17 Connect to a Remote SAS Server 1 Select Connect to remote SAS Server on in the Establish New Workspace Server Connection area. 2 Enter the machine name and port number in the appropriate boxes. 3 Click Connect. When the Open Workspace Server Connections area displays Current active connection followed by the remote SAS server information, you are connected to the SAS System. Open the Data Set Before you can begin an analysis, you need to open a data file for analysis. To open the airline data file: 1 Select SAS I Econometrics and Time Series I ETS Sample Data. The ETS Sample Files window appears. 2 Select Panel Models I airline. Create and Estimate the Base Model Open a New Analysis To start a panel data analysis, select SAS I Econometrics and Time Series I Fit Panel Data Regression. A Panel Data Analysis window appears. You specify the base model in this window. Assign Variables to Roles To specify a base model, you need to assign variables to roles. To assign a variable to a role: 1 Select the variable from the Select Columns list. 2 Click the appropriate role button in the Cast Selected Columns into Roles area. For this example, you need to assign lc as the response variable, I as the cross-sectional ID variable, and T as the time series ID variable. You also need to assign lq, lpf, and LF as the explanatory variables. These model specifications are shown in Figure 3.2.

24 18 Chapter 3: Getting Started with SAS Econometrics and Time Series Analysis for JMP Figure 3.2 Getting Started Example Base Model Specifications Estimate the Base Model After you have assigned all the relevant variables to roles, click OK to estimate the base model. Examine the Base Model Results After you specify and estimate the base model, the results window appears. You use the information in the results window to evaluate model fit and decide how to create alternative models. Data Summary The Data Summary area is at the top of the results window. It contains plots and tables of the observed data. In this area, you can examine the data for any trends or unusual observations. The information that appears in the Data Summary area depends on which analysis you select; this example shows the plots and tables included for a panel analysis. You can modify the view of the plots and tables in the Data Summary area by clicking on the red triangles next to the headings. You can also add plots or tables to the Data Summary area by clicking on the red triangles next to the headings. A Y vs Time plot of lc over time for each airline shows that overtime costs are increasing for all of the airlines. See Figure 3.3.

25 Examine the Base Model Results 19 Figure 3.3 Y By Time Plot in the Results Window Next is a Y vs Cross-Section plot of lc by airline for each time. Following these plots is a distribution plot and tables of the quantiles and summary statistics for lc. See Figure 3.4.

26 20 Chapter 3: Getting Started with SAS Econometrics and Time Series Analysis for JMP Figure 3.4 Distribution Plot and Fitted Models Area of the Results Window

Examine the Base Model Results 21 Fitted Models The Fitted Models area follows the Data Summary area. It contains a list of the models that have been estimated.

27 Examine the Base Model Results 21 Fitted Models The Fitted Models area follows the Data Summary area. It contains a list of the models that have been estimated. The model you estimated is called Model 1. Each model in the Fitted Models area has a model name, a check box for including the model in the Model Comparison area, the mean squared error (MSE) value for the model, the R-square measure, and a description of the model. When you click a model name, you can view the parameter estimates for that model in the Model Estimates area. Because only one model is estimated, the estimates for that model appear in the Model Estimates area. Model Estimates The last section of the results window is the Model Estimates area. The tables in the Model Estimates area depend on which analysis you select. For a panel analysis, the Model Estimates area contains tables for the Model Description, Fit Statistics, Parameter Estimates, Additional Results, and Panel Analysis Model Graphics. If you have also selected an option to produce SAS ODS graphs in the SAS Graphs Settings window (see the section SAS Graphs Settings Window on page 11), those graphs also appear. To evaluate the base model, you first examine the Fit Statistics table. Figure 3.5 shows the Fit Statistics table for the base model. Figure 3.5 Fit Statistics for the Base Model You see a large R-square in the Fit Statistics table, so there is evidence for good model fit. After examining the Fit Statistics table, you examine the parameter estimates in the Parameter Estimates area. See Figure 3.6.

28 22 Chapter 3: Getting Started with SAS Econometrics and Time Series Analysis for JMP Figure 3.6 Parameter Estimates for the Base Model There are several important results in the Parameter Estimates area: Most of the cross-sectional effects are highly significant (with the exception of CS2). This means that the cross sections are significantly different from the sixth cross section (which is the reference section). Many of the time effects show significance, but not uniformly.

29 Create an Alternative Model 23 The time dummy variables taper off in size and lose significance from time period 12 onward. As for the regression parameters: Output affects cost positively. Fuel price affects cost positively. Load factor output affects cost negatively. The unusual result is that the fuel cost is not significant. Based on these results, you decide to examine whether the results change if you ignore the effect of time and fit a one-way, cross-sectional fixed-effects model. Create an Alternative Model To create a one-way fixed-effects model, you open a dialog window called the Panel Data Analysis Options window. There are several ways to open a dialog window: Click the New Model button at the bottom of the Fitted Models area. Click the red triangle next to Fitted Models, and select New Model. Click the red triangle next to Model 1, and select Edit. If you open the dialog this way, change values, and click Ok in the dialog window, any results from the base model are erased, and you can no longer compare the base model with the new alternative model. Click the red triangle next to Model 1, and select Copy. A new model appears on the Fitted Models list; it is called Copy of Model 1. This model is identical to the base model, Model 1. To change this copy of Model 1 into a one-way fixed-effects model that ignores time, click the red triangle next to Copy of Model 1 and select Edit. After you open a dialog window, you change the model to a one-way, cross-sectional fixed-effects model by clicking the arrow next to Two-way and selecting One-Way, Cross-section. See Figure 3.7. Then click OK to estimate the model.

30 24 Chapter 3: Getting Started with SAS Econometrics and Time Series Analysis for JMP Figure 3.7 Alternative Model Specifications Compare the Base and Alternative Models After you estimate the alternative model, the results window is updated with the results for the alternative model. In the Fitted Models area, the list of the models contains Model 1 and Model 2. See Figure 3.8.

31 Compare the Base and Alternative Models 25 Figure 3.8 Fitted Model Area with the Base and Alternative Models Each model in the Fitted Models area has a model name, a check box for including the model in the Model Comparison area, the MSE value for the model, the R-square measure, and a description of the model. You can see that the MSE for Model 1 is lower, suggesting that model fit is better for Model 1 than Model 2. You select both check boxes in the Compare column to include both models in the Model Comparison area. You examine the Model Comparison area to decide which model is a better representation for the data. Figure 3.9 shows the Forecast Comparison Plot.

32 26 Chapter 3: Getting Started with SAS Econometrics and Time Series Analysis for JMP Figure 3.9 Forecast Comparison Plot with the Base and Alternative Models In this plot, the red line represents the observed lc, the green line represents the forecast from the base model, and the blue line represents the forecast for the alternative model. You can see that the forecasts for both models are nearly the same. Below the Forecast Comparison Plot is a Residual Comparison Plot, as shown in Figure 3.10.

33 Compare the Base and Alternative Models 27 Figure 3.10 Residual Comparison Plot with the Base and Alternative Models This plot contains the residuals for the base model (in red) and the alternative model (in blue). The red line for the base model appears to be more frequently closer to 0, which suggests that the forecast from base model is closer to the observed data. The Distribution Plot with Quantiles and Summary area contains plots and tables of the residuals for the base and alternative models. See Figure These tables and plots also indicate that the residuals for the alternative model tend to have greater variance and a wider range than those for the base model.

34 28 Chapter 3: Getting Started with SAS Econometrics and Time Series Analysis for JMP Figure 3.11 Response Residual Distribution Comparison for the Base and Alternative Models In addition to the Model Comparison area, you can also compare the base and alternative models by comparing model fit statistics and the model parameter estimates, which can be found in the Model Estimates area. To view the alternative model estimates in the Model Estimates area, click Model 2 in the Fitted Models area. As shown in Figure 3.12, the R-square statistic for the alternative model is still large, but the parameters change. The effect of fuel costs (lpf) comes in as very strong and significant. In addition, the coefficient for LF increases, although not as dramatically.

35 Compare the Base and Alternative Models 29 Figure 3.12 Fit Statistics and Parameter Estimates for the Alternative Model Overall, the model fit information and residual analysis suggest that base model has better fit.

36 30 Chapter 3: Getting Started with SAS Econometrics and Time Series Analysis for JMP Save and Open the Results Save Results After you build your models, you can save your work to a JMP project file by using the following steps: 1 Click the red triangle next to the Panel Data Analysis header. 2 Select Save Analysis. A Save Project As window appears. 3 In the Save Project As window, specify the name of the analysis and where you want the analysis to be saved. 4 Click Save. Open Results To open results: 1 Open JMP. 2 Open the saved JMP project file: In the JMP Home window, select FileI Open. Locate and select the saved JMP project file. Click Open. NOTE: You can also open the JMP project file from the file manager program. 3 The results window appears. References Greene, W. H. (2000), Econometric Analysis, 4th Edition, Upper Saddle River, NJ: Prentice-Hall.

37 Chapter 4 Fit Y by X with Autocorrelated and Heteroscedastic Errors Contents Overview of Fit Y by X with Autocorrelated and Heteroscedastic Errors Specify Autocorrelated Regression Analysis Step 1. Specify and Estimate a Base Model in the Initial Model Window Step 2. Examine Base Models Results in the Results Window Step 3. Create and Estimate an Alternative Model in the Options Window Autoregressive Error Regression Model Options Window Regressors Tab AR Model Tab GARCH Model Tab Hetero Tab Additional Tab Settings Windows Model Settings Window Comparison of Time Series Platform and Autocorrelated Regression Analysis Overview of Fit Y by X with Autocorrelated and Heteroscedastic Errors You select Fit Y by X with Autocorrelated and Heteroscedastic Errors to fit autocorrelated regression models. Autocorrelated regression models examine time series data when the errors are autocorrelated or heteroscedastic. The autoregressive error model corrects for autocorrelation. The generalized autoregressive conditional heteroscedasticity (GARCH) model and its variants model and correct for heteroscedasticity. Fit Y by X with Autocorrelated and Heteroscedastic Errors produces test statistics that can be used to diagnose the autocorrelation and heteroscedasticity of errors. After one or both of these aspects are identified, you can fit a model with autoregressive errors or a model that can account for heteroscedasticity. Fit Y by X with Autocorrelated and Heteroscedastic Errors supports the following models: generalized ARCH (GARCH) integrated GARCH (IGARCH) exponential GARCH (EGARCH) GARCH-in-mean (GARCH-M)

32 Chapter 4: Fit Y by X with Autocorrelated and Heteroscedastic Errors Fit Y by X with Autocorrelated and Heteroscedastic Errors can also analyze models that combine autoregressive errors and

38 32 Chapter 4: Fit Y by X with Autocorrelated and Heteroscedastic Errors Fit Y by X with Autocorrelated and Heteroscedastic Errors can also analyze models that combine autoregressive errors and GARCH-type heteroscedasticity by setting one or more variables as heteroscedastic. The first part of this chapter describes how to perform a Fit Y by X with Autocorrelated and Heteroscedastic Errors analysis. The second and third parts provide a detailed description of the associated options and settings windows. The final part of this chapter provides a comparison of Fit Y by X with Autocorrelated and Heteroscedastic Errors in SAS Econometrics and Time Series Analysis for JMP to the JMP Time Series platform. Specify Autocorrelated Regression Analysis Step 1. Specify and Estimate a Base Model in the Initial Model Window The base model for Fit Y by X with Autocorrelated and Heteroscedastic Errors has no autoregressive lags, no GARCH terms, and no heteroscedasticity variables. To specify and estimate a base model: 1 Open a data file. From the JMP Home window, select SAS I Econometrics and Time Series I ETS Sample Data. The ETS Sample Files window appears. (See Figure 4.1.) Select Autoregressive Models I argarchdata. Figure 4.1 ETS Sample Files Window

39 Step 1. Specify and Estimate a Base Model in the Initial Model Window 33 2 From the JMP Home window, select SAS I Econometrics and Time Series I Fit Y by X with Autocorrelated and Heteroscedastic Errors. The Autoregressive Error Regression Model initial model window appears. (See Figure 4.2.) Figure 4.2 Example Autoregressive Error Regression Model Window 3 Specify the Y (response) variable by selecting the variable in the Select Columns list and then clicking Y, Response. 4 (Optional) Specify any X (explanatory) variables by selecting the variables in the Select Columns list and then clicking X, Explanatory. You can select more than one variable by holding CTRL and clicking on each variable that you want to select. NOTE: The explanatory variables that you select from the initial model window become the master list for the subsequent models. You can only select a subset of explanatory variables from the master list as regressors; you cannot add new explanatory variables to the master list. 5 (Optional) Specify the ID (time) variable by selecting the variables in the Select Columns list and then clicking ID, Time. 6 Click OK to estimate the model.

40 34 Chapter 4: Fit Y by X with Autocorrelated and Heteroscedastic Errors Step 2. Examine Base Models Results in the Results Window After you create and estimate the base model, the Autoregressive Error Regression Model Results window appears. Figure 4.3 shows an example. Figure 4.3 Example Autoregressive Error Regression Model Results Window

41 Step 3. Create and Estimate an Alternative Model in the Options Window 35 The Autoregressive Error Regression Model Results window contains the following areas: The Data Summary area contains the original data in X-Y plot and a distribution plot with tables of the quantiles and summary statistics for the observed data. The Fitted Models area is similar for all analyses. For more information, see the section Results Window on page 5. The Model Comparison area is similar for all analyses. For more information, see the section Model Comparison Area on page 8. The Model Estimates area contains the following information: autoregression model estimates and tests for AR parameters autoregression model graphics You examine the Autoregressive Error Regression Model Results window to determine how to modify the base model to create an alternative model that is a better representation of your data. By clicking the red triangles next to headings in the results window, you can modify the view of the plots and tables shown or you can add more plots or tables to the results window. You can also collapse or expand sections by clicking the gray triangles next to the headings in this window. Step 3. Create and Estimate an Alternative Model in the Options Window 1 In the Autoregressive Error Regression Model Results window, you can open a Autoregressive Error Regression Model Options window (see Figure 4.4) to create a new model by doing one of the following: Click the New Model button at the bottom of the Fitted Models area. The Autoregressive Error Regression Model Options window appears with the current model settings. Click the red triangle next to the Fitted Models heading, and then select New Model. The Autoregressive Error Regression Model Options window appears with the current model settings. Click the red triangle next to Model 1 in the Fitted Models area, and select one of the following commands: Edit opens the Autoregressive Error Regression Model Options window. This window contains the current model settings. NOTE: If you choose this option and perform the remaining steps, you can no longer compare the base model to any alternative models. Copy creates a copy of the base model. Then click the red triangle next to Copy of Model 1, and select Edit to open the Autoregressive Error Regression Model Options window. This window contains the values of the copied model.

42 36 Chapter 4: Fit Y by X with Autocorrelated and Heteroscedastic Errors Figure 4.4 Regressors Tab of the Autoregressive Error Regression Model Options Window 2 In the Autoregressive Error Regression Model Options window, specify an alternative model. For more information about this window and its tabs, see the following section. 3 Click OK to estimate the alternative model. The Autoregressive Error Regression Model Options window closes, and the model results for the alternative model appear in the Autoregressive Error Regression Model Results window. For more information, see the section Results Window on page 5.

43 Autoregressive Error Regression Model Options Window 37 Autoregressive Error Regression Model Options Window The Autoregressive Error Regression Model Options window contains five tabs, which are described in the following sections. The options on each tab correspond to statements or options in the SAS/ETS AUTOREG procedure. Regressors Tab On the Regressors tab, you specify the X (explanatory) variables, which are often referred to as regressor variables. (See Figure 4.4.) To add a regressor variable to the model: 1 Select the variable in the Select Columns list. You can select more than one variable at a time by holding CTRL and clicking on each variable that you want to add. 2 Click. The variables that you select are moved from the Select Columns list to the Explanatory Variables list. To remove a regressor variable from the model: 1 Select the variable in the Explanatory Variables list. You can select more than one variable at a time by holding CTRL and clicking on each variable that you want to remove. 2 Click. The variables that you select are moved from the Explanatory Variables list to the Select Columns list. NOTE: You can compare models with different X variables, either by using the fitted or residual graphs or by using the overall model fit information (for example, Akaike s information criterion or the Bayesian information criterion) for each model. AR Model Tab On the AR Model tab, you specify the details of the autocorrelated regression process. See Figure 4.5.

44 38 Chapter 4: Fit Y by X with Autocorrelated and Heteroscedastic Errors Figure 4.5 AR Tab of the Autoregressive Error Regression Model Options Window The following options (which correspond to options in the MODEL statement of the AUTOREG procedure) are available on the AR Model tab: Order of AR process specifies the order of the autoregressive error process. This option corresponds to the NLAG= option. Remove nonsignificant AR parameters specifies whether to remove nonsignificant autoregressive parameters. The least significant parameters are removed first. This check box corresponds to the BACKSTEP option. GARCH Model Tab On the GARCH Model tab, you specify the details of the GARCH model. See Figure 4.6.

45 GARCH Model Tab 39 Figure 4.6 GARCH Model Tab of the Autoregressive Error Regression Model Options Window The following options (which correspond to options in the MODEL statement of the AUTOREG procedure) are available on the GARCH Model tab: P Q specifies the order of the process or the subset of GARCH terms to be fitted. This option corresponds to the P= option. specifies the order of the process or the subset of ARCH terms to be fitted. This option corresponds to the Q= option. Model type specifies the type of GARCH model. This option corresponds to the TYPE= option. The default is Nelson-Cao. Select one of the following from the Model type list: Nelson-Cao specifies the Nelson-Cao inequality constraints. Integrated specifies the integrated GARCH or IGARCH model. Nonnegative specifies the GARCH model with nonnegative constraints. Stationary constrains the sum of GARCH coefficients to be less than 1. Exponential specifies the exponential GARCH or EGARCH model.

40 Chapter 4: Fit Y by X with Autocorrelated and Heteroscedastic Errors Include intercept specifies whether to suppress the intercept parameter.

46 40 Chapter 4: Fit Y by X with Autocorrelated and Heteroscedastic Errors Include intercept specifies whether to suppress the intercept parameter. This option is available only when Integrated is selected from the Model type list. This check box corresponds to the NOINT option. Hetero Tab On the Hetero tab, you specify the heteroscedastic variance model. See Figure 4.7. The variables in the current data tables are displayed in the Select Columns list. You can select any of variables that are not used as X (regressor) and Y (dependent) variables. Figure 4.7 Hetero Tab of the Autoregressive Error Regression Model Options Window To add a heteroscedastic variable to the model: 1 Select the variable in the Select Columns list. You can select more than one variable at a time by holding CTRL and clicking on each variable that you want to add. 2 Click. The variables that you select are moved from the Select Columns list to the Heteroscedastic Variables list. To remove a heteroscedastic variable from the model: 1 Select the variable in the Explanatory Variables list. You can select more than one variable at a time by holding CTRL and clicking on each variable that you want to remove.

47 Additional Tab 41 2 Click. The variables that you select are moved from the Heteroscedastic Variables list to the Select Columns list. Additional Tab On the Additional tab, you specify the additional model settings. See Figure 4.8. Figure 4.8 Additional Tab of the Autoregressive Error Regression Model Options Window The following options (which correspond to options in the MODEL statement of the AUTOREG procedure) are available on the Additional tab: Include intercept in model specifies whether to suppress the intercept parameter. This check box corresponds to the NOINT option. Center dependent variable specifies whether to center the dependent variable for a model that does not have any explanatory variables. This check box corresponds to the CENTER option. This check box is available only when the model does not have regressors (explanatory variables).

48 42 Chapter 4: Fit Y by X with Autocorrelated and Heteroscedastic Errors Estimation Method specifies the estimation method. This option corresponds to the METHOD= option. Select one of the following from the Estimation Method list: Maximum Likelihood Estimates specifies maximum-likelihood estimation. Unconditional Least Squares Estimates specifies unconditional least squares estimation. Yule-Walker Estimates specifies Yule-Walker estimation. Iterative Yule-Walker Estimates specifies iterative Yule-Walker estimation. Covariance Matrix Type specifies the type of covariance matrix. This option corresponds to the COVEST= option. Select one of the following from the Covariance Matrix Type list: Outer Product Matrix specifies the outer product matrix. This is the default option. Hessian specifies the Hessian matrix. Quasi-Maximum Likelihood specifies the quasi-maximum likelihood method. HC0 specifies the Heteroscedasticity Consistent Covariance Matrix Estimator 0. This is equivalent to Quasi-Maximum Likelihood method. HC1 specifies the Heteroscedasticity Consistent Covariance Matrix Estimator 1. HC2 specifies the Heteroscedasticity Consistent Covariance Matrix Estimator 2. HC3 specifies the Heteroscedasticity Consistent Covariance Matrix Estimator 3. HC4 specifies the Heteroscedasticity Consistent Covariance Matrix Estimator 4. NEWEYWEST specifies the Newey-West estimator, a special heteroscedasticity- and autocorrelation-consistent (HAC) covariance matrix estimator. Settings Windows Fit Y by X with Autocorrelated and Heteroscedastic Errors analysis provides three settings windows. The SAS Graphs Settings window and Display Settings window are described in the section Add-in Main Menu on page 11. The Model Settings window is described in the following section. Model Settings Window The Model Settings window, shown in Figure 4.9, contains the options for model estimation and model constraints.

49 Model Settings Window 43 Figure 4.9 Model Settings Window Model Option Area The following options (which correspond to options in the MODEL statement of the AUTOREG procedure) are available in the Model Option area: Significance Level when Removing nonsignificant AR parameters specifies the significance level criterion for removing nonsignificant autoregressive parameters. This option corresponds to the SLSTAY= option. Maximum iterations specifies the maximum number of iterations. The default value is 50. This option corresponds to the MAXITER= option. Convergence criterion specifies the convergence criterion. This option corresponds to the CONVERGE= option.

50 44 Chapter 4: Fit Y by X with Autocorrelated and Heteroscedastic Errors GARCH Model Options Area The following options (which correspond to options in the MODEL statement of the AUTOREG procedure) are available in the GARCH Model Options area: Specify GARCH-M Form specifies the functional form of the GARCH-M model. GARCH=(MEAN= ) option. This option corresponds to the GARCH optimization specifies the type of GARCH model optimization. You can select the following values from the GARCH optimization list: Quasi-Newton specifies quasi-newton optimization. This option is the default option. Trust Region specifies trust region optimization. This option corresponds to the GARCH=(TR) option. Error Variance Model Options Area The following options (which correspond to options in the HETERO statement of the AUTOREG procedure) are available in the Error variance model options area: Include the unit term in the model specifies that the heteroscedasticity model not include the unit term for the functional form option. This option corresponds to the NOCONST option. Functional form specifies the functional form of the heteroscedasticity model. The functional form options are Exponential, Square, and Linear. By default, Exponential is selected. This option corresponds to the LINK= option. Constraints on estimated parameters specifies the constraints on the estimated parameters of the heteroscedastic model. The following options correspond to the values of the COEF= option: Nonnegative specifies that the heteroscedastic parameters must be nonnegative during model estimation. This option corresponds to COEF=NONNEG. Unit specifies that the heteroscdastic parameters be fixed to 1. This option corresponds to COEF=UNIT. Zero specifies that the heteroscdastic parameters be fixed to 0. This option corresponds to COEF=ZERO. Unrestricted specifies that the heteroscedastic parameters not be restricted during model estimation. This option corresponds to COEF=UNREST. By default, Nonnegative is selected when a GARCH model has been specified and Unrestricted is selected when no GARCH terms have been specified.

51 Comparison of Time Series Platform and Autocorrelated Regression Analysis 45 Constraints on estimated standard deviation specifies the constraints on the estimated standard deviation of the heteroscedastic model. The following options correspond to the values of the STD= option: Nonnegative specifies that the estimated standard deviation of the heteroscedastic model be nonnegative during model estimation. This option corresponds to STD=NONNEG. Unit specifies that the estimated standard deviation of the heteroscedastic model be fixed to 1. This option corresponds to STD=UNIT. Unrestricted specifies that the estimated standard deviation of the heteroscedastic model not be restricted during model estimation. This option corresponds to STD=UNREST. By default, Nonnegative is selected. Comparison of Time Series Platform and Autocorrelated Regression Analysis The JMP Time Series platform also analyzes autocorrelated data. However, there are several differences between the Time Series platform and the Fit Y by X with Autocorrelated and Heteroscedastic Errors analysis in the SAS Econometrics and Time Series Analysis for JMP. The JMP Time Series platform does not call a SAS procedure. It uses an ARIMA (Box-Jenkins) model to model and forecast time series. In contrast, Fit Y by X with Autocorrelated and Heteroscedastic Errors calls the SAS/ETS AUTOREG procedure, which performs regression analysis on variables with autocorrelated errors and supports ARCH and GARCH models to deal with heteroscedasticity. Table 4.1 briefly compares the JMP Time Series platform with the Fit Y by X with Autocorrelated and Heteroscedastic Errors analysis.

52 46 Chapter 4: Fit Y by X with Autocorrelated and Heteroscedastic Errors Table 4.1 Comparison of the JMP Time Series Platform and Fit Y by X with Autocorrelated and Heteroscedastic Errors Category JMP Time Series Platform Fit Y by X with Autocorrelated and Heteroscedastic Errors Model Box-Jenkins approach to estimating univariate models. Uses transfer functions when explanatory variables are present. Linear regression models, corrected for autocorrelated errors. ARCH/GARCH models, corrected for heteroscedasticity. Unit root tests Augmented Dickey-Fuller test. Phillips-Perron unit root test when there are no explanatory variables; the Phillips-Ouliaris cointegration test when there are explanatory variables. Order of lag User selects the order of the transfer function. Stepwise regression, which can automatically select the order of the autoregressive model by removing insignificant autoregressive parameters. Estimation Maximum likelihood estimation. Four different estimation methods. Residual plots Plot of AR residuals. Plots of AR and structural (OLS) residuals. Modeling options Time-series modeling options such as prewhitening, spectral density, variograms, and smoothing models. Does not provide these models. Profiler analysis No profiler plots of predicted values. Profiler plots for structural and AR models.

53 Chapter 5 Fit Count Data Regression Contents Overview of Fit Count Data Regression Specify Count Data Analysis Step 1. Specify and Estimate a Base Model in the Initial Model Window Step 2. Examine Base Model Results in the Results Window Step 3. Create and Estimate an Alternative Model in the Options Window Count Data Analysis Options Window Model Tab Zero-Inflated Model Tab Additional Tab Count Data Analysis Plots and Frequency Report Cumulative Probability Plot for Selected Counts Predicted Probability Plot for Selected Counts Model Average Probability vs Sample Probability Distribution Plot Model Average Probability vs Sample Probability Distribution Model Comparison Plot 59 Frequency Report Overview of Fit Count Data Regression You select Fit Count Data Regression to analyze regression models in which the dependent variable takes nonnegative integer (count) values. The dependent variable is usually an event count, which refers to the number of times an event occurs. For example, an event count might represent the number of ship accidents per year for a given fleet. Fit Count Data Regression supports the following models for count data: Poisson regression negative binomial regression with quadratic (NEGBIN2) and linear (NEGBIN1) variance functions zero-inflated Poisson (ZIP) model zero-inflated negative binomial (ZINB) model The first part of this chapter describes how to perform a Fit Count Data Regression analysis. The second part provides a detailed description of the associated options window. The third part describes several plots and a frequency report that are available for count data analysis.

54 48 Chapter 5: Fit Count Data Regression Specify Count Data Analysis Step 1. Specify and Estimate a Base Model in the Initial Model Window The base model for Fit Count Data Regression is the Poisson regression model. To specify and estimate a base model: 1 Open a data file. From the JMP Home window, select SAS I Econometrics and Time Series I ETS Sample Data. The ETS Sample Files window appears. (See Figure 5.1.) Select Count Models I CountRegLong97. Figure 5.1 ETS Sample Files Window 2 From the JMP Home window, select SAS I Econometrics and Time Series I Fit Count Data Regression. The Count Data Analysis initial model window appears. (See Figure 5.2.)

55 Step 2. Examine Base Model Results in the Results Window 49 Figure 5.2 Example Count Data Analysis Launch Window 3 Specify the Y (response) variable by selecting the variable in the Select Columns list and then clicking Y, Response. 4 (Optional) Specify any X (explanatory) variables by selecting the variables in the Select Columns list and then clicking X, Explanatory. You can select more than one variable by holding CTRL and clicking on each variable that you want to select. NOTE: The explanatory variables that you select from the initial model window become the master list for the subsequent models. You can only select a subset of explanatory variables from the master list as regressors; you cannot add new explanatory variables to the master list. 5 (Optional) Specify the offset variable by selecting the variable in the Select Columns list and then clicking Offset. 6 Click OK to estimate the model. Step 2. Examine Base Model Results in the Results Window After you create and estimate the base model, the Count Data Analysis Results window appears. See Figure 5.3.

56 50 Chapter 5: Fit Count Data Regression Figure 5.3 Example Count Data Analysis Results Window The Count Data Analysis Results window contains the following areas: The Data Summary area contains a Frequency Report with tables of statistics and a frequency plot for the observed count data. The Fitted Models area is similar for all analyses. For more information, see the section Fitted Models Area on page 6. The Model Comparison area is similar for all analyses. For more information about opening this area, see the section Model Comparison Area on page 8. The section Model Average Probability vs Sample Probability Distribution Model Comparison Plot on page 59 shows the comparison plot for Fit Count Data Regression.

Step 2. Examine Base Model Results in the Results Window 51 The Model Estimates area contains the following information: Cumulative Probability Plot for Selected Counts (see Figure 5.8.

57 Step 2. Examine Base Model Results in the Results Window 51 The Model Estimates area contains the following information: Cumulative Probability Plot for Selected Counts (see Figure 5.8.) Predicted Probability Plot for Selected Counts (see Figure 5.9.) Model Average Probability versus Sample Probability Distribution Plot (see Figure 5.10.) model estimates results: model fit summary, parameter estimates, and additional results See Figure 5.4 for an example of the Model Estimates area. Figure 5.4 Example Model Estimates Area in a Count Data Analysis Results Window You examine the Count Data Analysis Results window to determine how to modify the base model to create an alternative model that is a better representation of your data. You can modify the view of the plots by clicking the red triangles next to headings of the plots. You can also collapse or expand sections by clicking the gray triangles next to the headings in this window.

58 52 Chapter 5: Fit Count Data Regression Step 3. Create and Estimate an Alternative Model in the Options Window 1 In the Count Data Analysis Results window, you can open a Count Data Analysis Options window (see Figure 5.5) to create a new model by doing one of the following: Figure 5.5 Model Tab of the Count Data Analysis Options Window Click the New Model button at the bottom of the Fitted Models area. The Count Data Analysis Options window appears with the current model settings. Click the red triangle next to the Fitted Models header, and then select New Model. The Count Data Analysis Options window appears with the current model settings. Click the red triangle next to Model 1 in the Fitted Models area, and select one of the following commands: Edit opens the Count Data Analysis Options window. This window contains the current model settings. NOTE: If you choose this option and perform the remaining steps, you can no longer compare the base model to any alternative models. Copy creates a copy of the base model. Then click the red triangle next to Copy of Model 1, and select Edit to open the Count Data Analysis Options window. This window contains the values of the copied model. 2 In the Count Data Analysis Options window, specify an alternative model. For more information about this window and its tabs, see the following section.

59 Count Data Analysis Options Window 53 3 Click OK to estimate the alternative model. The Count Data Analysis Options window closes, and the model results for the alternative model appear in the Count Data Analysis Results window. For more information, see the section Results Window on page 5. Count Data Analysis Options Window The Count Data Analysis Options window contains three tabs, which are described in the following sections. The options on each tab correspond to statements or options in the SAS/ETS COUNTREG procedure. Model Tab On the Model tab, you specify the options for the MODEL statement in the COUNTREG procedure. (See Figure 5.5.) Model Variables specify the regressors in the model. To add a regressor variable to the model: 1 Select the variable in the Select Columns list. You can select more than one variable at a time by holding CTRL and clicking on each variable that you want to add. 2 Click. The variables that you select are moved from the Select Columns list to the Model Variables list. To remove a regressor variable from the model: 1 Select the variable in the Model Variables list. You can select more than one variable at a time by holding CTRL and clicking on each variable that you want to remove. 2 Click. The variables that you select are moved from the Model Variables list to the Select Columns list. NOTE: You can compare models with different X variables, either by using the overall model fit information (for example, Akaike s information criterion or the Bayesian information criterion) for each model or by using the model comparison graph. Distribution specifies the type of model to be analyzed. This option corresponds to the DIST= option. No Intercept in Model specifies whether to suppress the intercept parameter. This check box corresponds to the NOINT option.

54 Chapter 5: Fit Count Data Regression Zero-Inflated Model Tab On the Zero-Inflated Model tab, you specify the options for the ZEROMODEL statement in the COUN- TREG procedure. See Figure 5.6.

60 54 Chapter 5: Fit Count Data Regression Zero-Inflated Model Tab On the Zero-Inflated Model tab, you specify the options for the ZEROMODEL statement in the COUN- TREG procedure. See Figure 5.6. Figure 5.6 Zero-Inflated Model Tab of the Count Data Analysis Options Window Zero-Inflated Variables specify the regressors for a zero-inflated model. To add a regressor variable to the zero-inflated model: 1 Select the variable in the Select Columns list. You can select more than one variable at a time by holding CTRL and clicking on each variable that you want to add. 2 Click. The variables that you select are moved from the Select Columns list to the Zero- Inflated Variables list. To remove a regressor variable from the zero-inflated model: 1 Select the variable in the Zero-Inflated Variables list. You can select more than one variable at a time by holding CTRL and clicking on each variable that you want to remove.

61 Additional Tab 55 2 Click. The variables that you select are moved from the Zero-Inflated Variables list to the Select Columns list. Link Function specifies the distribution function used to compute probability of zeros. This option corresponds to the LINK= option in the ZEROMODEL statement. The default is Logistic. Select one of the following from the Link Function list: Logistic specifies the logistic distribution. Normal specifies the standard normal distribution. Additional Tab On the Additional tab, you specify additional options for the COUNTREG procedure. See Figure 5.7. Figure 5.7 Additional Tab of the Count Data Analysis Options Window The following options (which correspond to options in the PROC COUNTREG statement of the COUNTREG procedure) are available on the Additional tab:

62 56 Chapter 5: Fit Count Data Regression Covariance Matrix specifies the type of covariance matrix of the parameter estimates. This option corresponds to the COVEST= option. The default is Hessian. Select one of the following from the Covariance Matrix list: Outer Product Matrix specifies the covariance from the outer product matrix. Hessian specifies the covariance from the Hessian matrix. Outer Product/Hessian specifies the covariance from the outer product and Hessian matrices. Optimization Method specifies the iterative minimization method to use. This option corresponds to the METHOD= option. The default is Newton-Raphson. Select one of the following from the Optimization Method list: Conjugate-Gradient specifies the conjugate-gradient method. Double-Dogleg specifies the double-dogleg method. Quasi-Newton specifies the quasi-newton method. Nelder-Mead Simplex specifies Nelder-Mead simplex method. Newton-Raphson specifies the Newton-Raphson method. Newton-Raphson Ridge specifies the Newton-Raphson ridge method. Trust Region specifies the trust region method. Count Data Analysis Plots and Frequency Report After you create and estimate a model, the Count Data Analysis Results window appears. It displays the plots and a frequency report described in the following subsections. Cumulative Probability Plot for Selected Counts Figure 5.8 shows the cumulative probability plot of the response variable that takes values that are specified by the Counts boxes at the bottom of the window.

63 Cumulative Probability Plot for Selected Counts 57 Figure 5.8 Cumulative Probability Plot for Selected Counts In the control panel located below the X-axis label, you can analyze data from different perspectives by selecting different values for the X-axis variable and selecting different values for the count range. For example, you might be interested in addressing question such as, What is the cumulative probability that the scientist will publish fewer than two articles if the number of articles published by the scientist s mentor is 10? You can find the answer from the plot by selecting the X-axis variable ment and setting the count range to Œ0; 2.

64 58 Chapter 5: Fit Count Data Regression Predicted Probability Plot for Selected Counts Figure 5.9 shows the predicted probability plot of the response variable that uses the estimated model and takes the current count value (when the current count value is within the selected count value range). Figure 5.9 Predicted Probability Plot for Selected Counts In the control panel located below the X-axis label, you can analyze data from different perspectives by selecting different values for the X-axis variable and selecting different values for the count range. For example, Figure 5.9 shows a way to find how the number of articles published by the scientist s mentor affect the predicted probability that the scientist will publish less than two articles.

65 Model Average Probability versus Sample Probability Distribution Model Comparison Plot 59 Model Average Probability versus Sample Probability Distribution Plot Figure 5.10 shows a plot that compares the sample probability distribution of the observed data to the average probability distributions that are predicted by using the estimated model. Figure 5.10 Model Average Probability versus Sample Probability Distribution Plot Model Average Probability versus Sample Probability Distribution Model Comparison Plot Figure 5.11 shows a plot that compares the sample probability distribution of the observed data to the average probability distributions that are predicted by using the models that are selected from the Fitted Models control panel.

66 60 Chapter 5: Fit Count Data Regression Figure 5.11 Model Average Probability versus Sample Probability Distribution Model Comparison Plot Frequency Report The Frequency Report in the Data Summary area (see Figure 5.3) shows some summary statistics about the observed count data. In addition, it includes a table that shows the frequency, the sample probability, and a histogram-like chart of the count data. You can click any row in that table, and the corresponding observations are highlighted in the original data table. Select the Hide Zero Frequencies check box to hide count values that have zero frequency in this table; clear the Hide Zero Frequencies check box to show count values that have zero frequency.

67 Chapter 6 Fit Panel Data Regression Contents Overview of Fit Panel Data Regression Specify a Panel Analysis Model Step 1. Specify and Estimate a Base Model in the Initial Model Window Step 2. Examine Base Model Results in the Results Window Step 3. Create and Estimate an Alternative Model in the Options Window Panel Data Regression Options Window Model Tab Regressors Tab Overview of Fit Panel Data Regression You select Fit Panel Data Regression to perform panel data analysis. Panel data analysis is a class of linear econometric models that commonly arise when time series and cross-sectional data are combined. Typical examples of panel data include observations over time in households, countries, firms, trade, and so on. For example, survey data on household income is panel data when the same households are repeatedly surveyed at multiple times (for example, over several years). Panel data analysis models can be grouped into several categories depending on the structure of the error term. Some examples of panel data analysis models that can be fit with Fit Panel Data Regression are: one-way and two-way models fixed-effects and random-effects models autoregressive models moving average models The first part of this chapter describes how to perform a Fit Panel Data Regression analysis. The second part provides a detailed description of the windows that are associated with Fit Panel Data Regression. There is no unique Settings window for Fit Panel Data Regression; see the section SAS Graphs Settings Window on page 11 and section Display Settings Window on page 12 for all the relevant information about settings windows for this analysis.

68 62 Chapter 6: Fit Panel Data Regression Specify a Panel Analysis Model Step 1. Specify and Estimate a Base Model in the Initial Model Window The base model for Fit Panel Data Regression is a model with an intercept and two-way fixed effects. To specify and estimate a base model: 1 Open a data file. From the JMP Home window, select SAS I Econometrics and Time Series I ETS Sample Data. The ETS Sample Files window appears (see Figure 6.1.) Select Panel Models I greene. Figure 6.1 ETS Sample Files Window 2 From the JMP Home window, select SAS I Econometrics and Time Series I Fit Panel Data Regression. The Panel Data Analysis initial model window appears. See Figure 6.2.

69 Step 2. Examine Base Model Results in the Results Window 63 Figure 6.2 Example Initial Model Window for Fit Panel Data Regression 3 Specify the Y (response) variable by selecting the variable in the Select Columns list and then clicking Y, Response. 4 (Optional) Specify any X (explanatory) variables by selecting the variables in the Select Columns list and then clicking X, Explanatory. You can select more than one variable by holding CTRL and clicking on each variable that you want to select. 5 Specify a cross-sectional ID variable by selecting the variable in the Select Columns list and then clicking Cross-Sectional ID. 6 Specify a time-series ID variable by selecting the variable in the Select Columns list and then clicking Time-Series ID. 7 Click OK to estimate the model. Step 2. Examine Base Model Results in the Results Window After you create and estimate the base model, the Panel Data Analysis Results window appears. See Figure 6.3.

70 64 Chapter 6: Fit Panel Data Regression Figure 6.3 Example Panel Data Analysis Results Window

71 Step 2. Examine Base Model Results in the Results Window 65 The Panel Data Analysis Results window contains the following areas: The Data Summary area contains the original data in a Y Time Plot and a Y Cross-Section Plot. It also contains tables of the quantiles and summary statistics for the observed data. The Fitted Models area is similar for all analyses. For more information, see the section Fitted Models Area on page 6. The Model Comparison area is similar for all analyses. For more information, see the section Model Comparison Area on page 8. The Model Estimates area contains the following information: model estimates results: model description, fit statistics, and parameter estimates additional results panel analysis model graphics See Figure 6.4 for an example of the Model Estimates area.

72 66 Chapter 6: Fit Panel Data Regression Figure 6.4 Example Model Estimates Area in a Panel Data Analysis Results Window You examine the Panel Data Analysis Results window to determine how to modify the base model to create an alternative model that is a better representation of your data. You can modify the plots and tables shown by clicking the red triangles next to headings in the results window. You can also collapse or expand sections by clicking the gray triangles next to the headings in this window.

73 Step 3. Create and Estimate an Alternative Model in the Options Window 67 Step 3. Create and Estimate an Alternative Model in the Options Window 1 In the Panel Data Analysis Results window, you can open a Panel Data Analysis Options window (see Figure 6.5) to create a new model by doing one of the following: Click the New Model button at the bottom of the Fitted Models area. The Panel Data Analysis Options window appears with the current model settings. Click the red triangle next to the Fitted Models heading, and then select New Model. The Panel Data Analysis Options window appears with the current model settings. Figure 6.5 Example Panel Data Analysis Options Window Click the red triangle next to Model 1 in the Fitted Models area, and select one of the following commands: Edit opens the Panel Data Analysis Options window. This window contains the current model settings. NOTE: If you choose this option and perform the remaining steps, you can no longer compare the base model to any alternative models. Copy creates a copy of the base model. Then click the red triangle next to Copy of Model 1,

74 68 Chapter 6: Fit Panel Data Regression and select Edit to open the Panel Data Analysis Options window. This window contains the values for the copied model. 2 In the Panel Data Analysis Options window, specify an alternative model. For more information about this window and its tabs, see the following section. 3 Click OK to estimate the alternative model. The Panel Data Analysis Options window closes, and the model results for the alternative model appear in the Panel Data Analysis Results window. For more information, see the section Results Window on page 5. Panel Data Regression Options Window The Panel Data Analysis Options window contains two tabs, which are described in the following sections. The options on these tabs correspond to statements or options for the SAS/ETS PANEL procedure. Model Tab On the Model tab, you specify the model type and options. An example of the Model tab is shown in Figure 6.5. Select one of the following options from the Model Type list (these options correspond to the options in the MODEL statement of the PANEL procedure): Fixed Effects specifies that a fixed effects model be estimated. Fixed effects can be one-way cross-sectional, one-way time, or two-way. These options correspond to the FIXONE, FIXONETIME, and FIXTWO options, respectively. Random-Effects specifies that a random effects model be estimated. Random effects can be one-way or two-way. These options correspond to the RANONE and RANTWO options, respectively. Between Groups specifies that a between-groups model be estimated. This option corresponds to the BTWNG option. Between Time Periods specifies that a between-time-periods model be estimated. This option corresponds to the BTWNT option. Da Silva specifies that the model be estimated using the Da Silva method, which assumes a mixed variancecomponent moving average model for the error structure. This option corresponds to the DASILVA option. Parks specifies that the model be estimated using the Parks method, which assumes a first-order autoregressive model for the error structure. This option corresponds to the PARKS option.

75 Model Tab 69 Pooled specifies that a pooled (OLS) model be estimated. This option corresponds to the POOLED option. The options in the model details area depend on which model type you select. These options correspond to the options in the MODEL statement of the PANEL procedure. The following options can appear in the model details area: Covariance Matrix Estimator specifies the type of covariance matrix estimator: Newey and West specifies the well-known Newey-West estimator, a special heteroscedasticity- and autocorrelationconsistent (HAC) covariance matrix estimator. This option corresponds to the NEWEYWEST option. OLS Estimator specifies the simple OLS estimator. This option corresponds to the HCCME=NO option. HCCME0 specifies the Heteroscedasticity-Corrected Covariance Matrix Estimator type 0. This option corresponds to the HCCME=0 option. HCCME1 specifies the Heteroscedasticity-Corrected Covariance Matrix Estimator type 1. This option corresponds to the HCCME=1 option. HCCME2 specifies the Heteroscedasticity-Corrected Covariance Matrix Estimator type 2. This option corresponds to the HCCME=2 option. HCCME3 specifies the Heteroscedasticity-Corrected Covariance Matrix Estimator type 3. This option corresponds to the HCCME=3 option. HCCME4 specifies the Heteroscedasticity-Corrected Covariance Matrix Estimator type 4. This option corresponds to the HCCME=4 option. Cluster Correction specifies the cluster correction for the variance-covariance matrix. The cluster correction can be requested with HCCME=0, 1, 2 or 3. This check box corresponds to the CLUSTER option. Include intercept in model specifies whether to suppress the intercept parameter from the model. This check box corresponds to the NOINT option. Variance Estimation specifies the type of variance component estimate to use for random effects. This option corresponds to the VCOMP= option. The default is Fuller-Battese (VCOMP=FB) for balanced data and Wansbeek- Kapteyn (VCOMP=WK) for unbalanced data. One-way Breusch-Pagan test specifies whether to perform the Breusch-Pagan one-way test for random effects. This check box corresponds to the BP option.

76 70 Chapter 6: Fit Panel Data Regression Two-way Breusch-Pagan test specifies whether to perform the Breusch-Pagan two-way test for random effects. This check box corresponds to the BP2 option. Order of Moving Average specifies the order of the moving average process in the Da Silva method. This option corresponds to the M= option. The default is 1. PHI matrix of covariance estimates specifies whether to print the ˆ matrix of estimated covariances of the observations for the Parks method. The PHI option is relevant only when the PARKS option is used. This check box corresponds to the PHI option. Autocorrelation coefficient estimates specifies whether to print the estimated autocorrelation coefficients for the Parks method. This check box corresponds to the RHO option. Regressors Tab On the Regressors tab, you specify the X (explanatory) variables, which are often referred to as regressor variables. An example of the Regressors tab is shown in Figure 6.6.

Regressors Tab 71 Figure 6.6 Panel Data Analysis Options Window with the Regressors Tab To add a regressor variable to the model: 1 Select the variable in the Select Columns list.

77 Regressors Tab 71 Figure 6.6 Panel Data Analysis Options Window with the Regressors Tab To add a regressor variable to the model: 1 Select the variable in the Select Columns list. You can select more than one variable at a time by holding CTRL and clicking on each variable that you want to add. 2 Click. The variables that you select are moved from the Select Columns list to the Explanatory Variables list. To remove a regressor variable from the model: 1 Select the variable in the Explanatory Variables list. You can select more than one variable at a time by holding CTRL and clicking on each variable that you want to remove. 2 Click. The variables that you select are moved from the Model Variables list to the Select Columns list. NOTE: Models with different X variables can be compared, either by using the fitted or residual graphs or by using the overall model fit information (for example, AIC or BIC) for each model.

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79 Chapter 7 Model Severity of an Event Contents Overview of Model Severity of an Event Specify Severity Data Analysis Step 1. Specify and Estimate a Base Model in the Initial Model Window Step 2. Examine Base Model Results in the Results Window Step 3. Create and Estimate an Alternative Model in the Options Window Severity Data Analysis Options Window Scale Model Tab Distribution Tab Estimation Options Tab Severity Data Analysis Plots Estimates of EDF and CDF Plot for the Selected Distribution Estimates of PDF Plot for the Selected Distribution P-P Plot for the Selected Distribution Model Comparison Plot: Estimates of EDF and CDF Model Comparison Plot: Estimates of PDF Overview of Model Severity of an Event You select Model Severity of an Event to estimate parameters of any arbitrary continuous probability distribution that is used to model the magnitude (severity) of a continuous-valued event of interest. Some examples of such events are loss amounts paid by an insurance company and demand of a product as depicted by its sales. Model Severity of an Event is especially useful when the severity of an event does not follow typical distributions, such as the normal distribution, that are often assumed by standard statistical methods. Model Severity of an Event provides the following 10 different predefined probability distribution models: Burr (BURR) exponential (EXP) gamma (GAMMA) generalized Pareto (GPD) inverse Gaussian (IGAUSS)

80 74 Chapter 7: Model Severity of an Event lognormal (LOGN) Pareto (PARETO) Tweedie (TWEEDIE) scaled Tweedie (STWEEDIE) Weibull (WEIBULL) Model Severity of an Event can fit multiple distributions at the same time and choose the best distribution according to a specified selection criterion. Seven different statistics of fit can be used as selection criteria: log likelihood, Akaike s information criterion (AIC), corrected Akaike s information criterion (AICC), Schwarz Bayesian information criterion (BIC), Kolmogorov-Smirnov statistic (KS), Anderson-Darling statistic (AD), and Cramér-von Mises statistic (CvM). Model Severity of an Event provides the following key features: It enables you to fit a distribution model when the severity values are truncated or censored or both. You can specify any combination of the following types of censoring and truncation effects: left-censoring, right-censoring, left-truncation, or right-truncation. This is especially useful in applications that use an insurance-type model where a severity (loss) is reported and recorded only if it is greater than the deductible amount (left-truncation) and where a severity value greater than or equal to the policy limit is recorded at the limit (right-censoring). Another useful application is that of interval-censored data, where you know both the lower limit (right-censoring) and upper limit (left-censoring) on the severity, but you do not know the exact value. It enables you to define any arbitrary continuous parametric distribution model and to estimate its parameters. You just need to define the key components of the distribution, such as its probability density function (PDF) and cumulative distribution function (CDF), as a set of functions and subroutines written with the FCMP procedure, which is part of Base SAS software. It can model the effect of regressor variables on a probability distribution, as long as the distribution has a scale parameter. A linear combination of the regressor variables is assumed to affect the scale parameter via an exponential link function. The first part of this chapter describes how to perform a Model Severity of an Event analysis. The second part provides a detailed description of the associated options window. The third part describes several plots that are available for severity data analysis.

81 Step 1. Specify and Estimate a Base Model in the Initial Model Window 75 Specify Severity Data Analysis Step 1. Specify and Estimate a Base Model in the Initial Model Window By default, Model Severity of an Event fits the following 8 predefined distribution models: Burr, exponential, gamma, generalized Pareto, inverse Gaussian, lognormal, Pareto, and Weibull. To specify and estimate a base model: 1 Open a data file. From the JMP Home window, select SAS I Econometrics and Time Series I ETS Sample Data. The ETS Sample Files window appears. (See Figure 7.1.) Select Severity Models I SeverityDemo. Figure 7.1 ETS Sample Files Window 2 From the JMP Home window, select SAS I Econometrics and Time Series I Model Severity of an Event. The Severity Data Analysis initial model window appears. (See Figure 7.2.)

82 76 Chapter 7: Model Severity of an Event Figure 7.2 Example Initial Model Window for Severity Data Analysis 3 Specify the Y (response) variable by selecting the variable in the Select Columns list and then clicking Y, Response. 4 (Optional) Specify any regressor variables for scale parameter by selecting the variables in the Select Columns list and then clicking X, Explanatory. You can select more than one variable by holding CTRL and clicking on each variable that you want to add. NOTE: The regressor variables that you select from the initial model window become the master list for the subsequent models. You can only select a subset of regressor variables from the master list; you cannot add new regressor variables to the master list. 5 (Optional) If available, specify the left-censoring variable by selecting the variable in the Select Columns list and then clicking Left-censoring.

83 Step 2. Examine Base Model Results in the Results Window 77 6 (Optional) If available, specify the right-censoring variable by selecting the variable in the Select Columns list and then clicking Right-censoring. 7 (Optional) If available, specify the left-truncation variable by selecting the variable in the Select Columns list and then clicking Left-truncation. 8 (Optional) If available, specify the right-truncation variable by selecting the variable in the Select Columns list and then clicking Right-truncation. 9 (Optional) If available, specify the weight variable by selecting the variable in the Select Columns list and then clicking Weight Variable. 10 Click OK to estimate the model. Step 2. Examine Base Model Results in the Results Window After you create and estimate the default model, the Severity Data Analysis Results window appears. (See Figure 7.3.) The Severity Data Analysis Results window contains the following areas: The Data Summary area contains a Descriptive Statistics table, a distribution plot with a smooth curve (kernel density estimate) overlaid on the histogram, a slider to control the amount of smoothing for the smooth curve, a Summary Statistics table, and a CDF Plot for the response variable. The Fitted Models area is similar for all analyses. For more information, see the section Fitted Models Area on page 6. NOTE: For severity data analysis, there are usually multiple distributions for each model. Each line in Fitted Models area represents a distribution model. The Model Comparison area is similar for all analyses. For more information about opening this area, see the section Model Comparison Area on page 8. The sections Model Comparison Plot: Estimates of EDF and CDF on page 88 and Model Comparison Plot: Estimates of PDF on page 89 show comparison plots for Model Severity of an Event.

84 78 Chapter 7: Model Severity of an Event Figure 7.3 Example Severity Data Analysis Results Window The Model Estimates area contains the following information for each distribution: distribution information model estimates results: fit statistics and parameter estimates estimates of the EDF and CDF plots (see Figure 7.8) estimates of the PDF plot (see Figure 7.9)

85 Step 2. Examine Base Model Results in the Results Window 79 P-P plot (see Figure 7.10) See Figure 7.4 for an example of the Model Estimates area. Figure 7.4 Example Model Estimates Area in a Severity Data Analysis Results Window You examine the Severity Data Analysis Results window to determine how to modify the base model to create an alternative model that is a better representation of your data. You can modify the view of the plots by clicking the red triangles next to headings of the plots. You can also collapse or expand sections by clicking the gray triangles next to the headings in this window.

86 80 Chapter 7: Model Severity of an Event Step 3. Create and Estimate an Alternative Model in the Options Window 1 In the Severity Data Analysis Results window, you can open a Severity Data Analysis Options window (see Figure 7.5) to create a new model by doing one of the following: Figure 7.5 Scale Model Tab of the Severity Data Analysis Options Window Click the New Model button at the bottom of the Fitted Models area. The Severity Data Analysis Options window appears with the current model settings. Click the red triangle next to the Fitted Models heading, and then select New Model. The Severity Data Analysis Options window appears with the current model settings. Click the red triangle next to Model 1 in the Fitted Models area, and select one of the following commands: Edit opens the Severity Data Analysis Options window. This window contains the current model settings. NOTE: If you choose this option and perform the remaining steps, you can no longer compare the base model to any alternative models.

87 Severity Data Analysis Options Window 81 Copy creates a copy of the base model. Then click the red triangle next to Copy of Model 1, and select Edit to open the Severity Data Analysis Options window. This window contains the values of the copied model. 2 In the Severity Data Analysis Options window, specify an alternative model. For more information about this window and its tabs, see the following section. 3 Click OK to estimate the alternative model. The Severity Data Analysis Options window closes, and the model results for the alternative model appear in the Severity Data Analysis Results window. For more information, see the section Results Window on page 5. Severity Data Analysis Options Window The Severity Data Analysis Options Window contains three tabs, which are described in the following sections. The options on each tab correspond to statements or options in the SAS/ETS SEVERITY procedure. Scale Model Tab On the Scale Model tab, you specify the options that correspond to the SCALEMODEL statement in the SEVERITY procedure. (See Figure 7.5.) Explanatory Variables specifies the regressor variables in the model. To add a regressor variable to the scale model: 1 Select the variable in the Select Columns list. You can select more than one variable at a time by holding CTRL and clicking on each variable that you want to add. 2 Click. The variables that you select are moved from the Select Columns list to the Explanatory Variables list. To remove a regressor variable from the scale model: 1 Select the variable in the Explanatory Variables list. You can select more than one variable at a time by holding CTRL and clicking on each variable that you want to remove. 2 Click. The variables that you select are moved from Explanatory Variables list to the Select Columns list. NOTE: You can compare models with different regressor variables, either by using the overall model fit information (for example, Akaike s information criterion or the Bayesian information criterion) for each model or by using the model comparison graph.

82 Chapter 7: Model Severity of an Event Distribution Tab On the Distribution tab, you specify the options that correspond to the DIST statement in the SEVERITY procedure. See Figure 7.

88 82 Chapter 7: Model Severity of an Event Distribution Tab On the Distribution tab, you specify the options that correspond to the DIST statement in the SEVERITY procedure. See Figure 7.6. Figure 7.6 Distribution Tab of the Severity Data Analysis Options Window Distribution To add a distribution to the Selected Distributions list: 1 Select the distribution in the Candidate Distributions list. You can select more than one distribution at a time by holding CTRL and clicking on each distribution that you want to add. 2 Click. The distributions that you select are moved from Candidate Distributions list to the Selected Distributions list. To remove a distribution from the Selected Distributions list: 1 Select the distribution in the Selected Distributions list. You can select more than one distribution at a time by holding CTRL and clicking on each distribution that you want to remove. 2 Click. The distributions that you select are moved from Selected Distributions list to the Candidate Distributions list.

89 Estimation Options Tab 83 Estimation Options Tab On the Estimation Options tab, you specify the options that are related to estimation. See Figure 7.7. Figure 7.7 Estimation Options Tab of the Severity Data Analysis Options Window

90 84 Chapter 7: Model Severity of an Event The following options (which correspond to options in the PROC SEVERITY statement) are available on the Estimation Options tab: EDF specifies the method for computing the nonparametric or empirical estimate of the cumulative distribution function of the data. This option corresponds to the EDF= option. The default is AUTO. Select one of the following from the EDF list: AUTO specifies that the method be chosen automatically based on the data specification. STD specifies the standard empirical estimation method. You cannot specify this method when both right-censoring and left-censoring are specified. KM specifies the product limit estimator method proposed by Kaplan and Meier. You cannot specify this method when you specify both right-censoring and left-censoring. MKM specifies the modified product limit estimator method. You cannot specify this method when you specify both right-censoring and left-censoring. This method allows Kaplan-Meier s product limit estimates to be more robust by ignoring the contributions to the estimate due to small risk-set sizes. The minimum risk-set size that makes it eligible to be included in the estimation can be specified either as an absolute lower bound on the size (the RSLB= option) or a relative lower bound that is determined by the formula cn. Values of c and can be specified by using the C= and ALPHA= options, respectively. By default, the relative lower bound is used with values of c D 1 and D 0:5. However, you can modify the default by using the following options: C specifies the value to use for when the lower bound on the risk set size is defined as cn. This value must satisfy 0 < < 1. ALPHA specifies the value to use for C when the lower bound on the risk set size is defined as cn. This value must satisfy C > 0. RSLB specifies the absolute lower bound on the risk set size to be included in the estimate. Variance Divisor specifies the denominator to use for computing the covariance estimates. This option corresponds to the VARDEF= option. The default is Degrees of Freedom. Select one of the following from the Variance Divisor list: Degrees of Freedom specifies that the number of nonmissing observations minus the model degrees of freedom (number of parameters) be used. Number of Observations specifies that the number of nonmissing observations be used.

Estimates of EDF and CDF Plot for the Selected Distribution 85 Severity Data Analysis Plots After you create and estimate a model, the Severity Data Analysis Results window appears.

91 Estimates of EDF and CDF Plot for the Selected Distribution 85 Severity Data Analysis Plots After you create and estimate a model, the Severity Data Analysis Results window appears. It displays the plots described in the following subsections. Estimates of EDF and CDF Plot for the Selected Distribution Figure 7.8 shows a plot of the cumulative distribution function (CDF) estimates of the selected distribution model and the empirical distribution function (EDF) estimate. Figure 7.8 Estimates of EDF and CDF Plot for the Selected Distribution

92 86 Chapter 7: Model Severity of an Event Estimates of PDF Plot for the Selected Distribution Figure 7.9 shows a plot of the probability density function (PDF) estimates of the selected distribution model and the nonparametric kernel and histogram estimates. Figure 7.9 Estimates of PDF Plot for the Selected Distribution

93 P-P Plot for the Selected Distribution 87 P-P Plot for the Selected Distribution Figure 7.10 shows the probability-probability plot (known as the P-P plot) that compares the CDF estimate of the selected distribution model against the empirical distribution function (EDF). Figure 7.10 P-P Plot for the Selected Distribution

94 88 Chapter 7: Model Severity of an Event Model Comparison Plot: Estimates of EDF and CDF Figure 7.11 shows a plot that compares the empirical distribution function (EDF) of the observed data to the cumulative distribution function (CDF) estimates of the models that are selected from the Fitted Models control panel. Figure 7.11 Model Comparison Plot: Estimates of EDF and CDF

95 Model Comparison Plot: Estimates of PDF 89 Model Comparison Plot: Estimates of PDF Figure 7.12 shows a plot that compares the nonparametric kernel and histogram estimates of the observed data to the probability density function (PDF) estimates of the models that are selected from Fitted Models control panel. Figure 7.12 Model Comparison Plot: Estimates of PDF

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97 Chapter 8 Fit Instrumental Variables Regression Contents Overview of Fit Instrumental Variables Regression Specify Instrumental Variables Regression Analysis Step 1. Specify and Estimate a Base Model in the Initial Model Window Step 2. Examine Base Model Results in the Results Window Step 3. Create and Estimate an Alternative Model in the Options Window Instrumental Variables Regression Options Window Model Tab Settings Windows Model Settings Window Overview of Fit Instrumental Variables Regression You select Fit Instrumental Variables Regression to fit a model that has endogenous regressors, that is, explanatory variables correlated with the regression error term. Such correlation can occur when the dependent variable causes at least one of the covariates ( reverse causation), when relevant explanatory variables are omitted from the model, or when the covariates are subject to measurement error. In these situations, ordinary linear regression generally produces biased and inconsistent estimates. However, if an instrument variable is available, consistent estimates can still be obtained. In linear models, a valid instrumental variable must satisfy two conditions: The instrument must be correlated with the endogenous explanatory variables, conditional on the other covariates. The instrument cannot be correlated with the error term in the explanatory equation. The general instrumental variables regression model has four types of variables: the dependent variable; problematic endogenous regressors, which are potentially correlated with the error term; additional regressors, called included exogenous variables, that are not correlated with the error term; and instrumental variables. For instrumental variables regression to be possible, there must be at least as many instrumental variables as endogenous regressors. Fit Instrumental Variables Regression provides the following estimation methods: ordinary least squares estimation (OLS; this is the default) two-stage least squares estimation (2SLS)

92 Chapter 8: Fit Instrumental Variables Regression limited information maximum likelihood estimation (LIML) The first part of this chapter describes how to perform a Fit Instrumental Variables

98 92 Chapter 8: Fit Instrumental Variables Regression limited information maximum likelihood estimation (LIML) The first part of this chapter describes how to perform a Fit Instrumental Variables Regression analysis. The second and third parts provide a detailed description of the windows that are associated with Fit Instrumental Variables Regression. Specify Instrumental Variables Regression Analysis Step 1. Specify and Estimate a Base Model in the Initial Model Window The base model performs OLS regression by default. The initial base model merely provides a starting point for the subsequent analysis. The instrumental variables regression analysis does not really start until you create a new model that specify a subset of variables to be used as regressors and specify excluded exogenous variables to be used as instrumental variables. The base model also provides a reference for model comparison purpose. To specify and estimate a base model: 1 Open a data file. From the JMP Home window, select SAS I Econometrics and Time Series I ETS Sample Data. The ETS Sample Files window appears. (See Figure 8.1.) Select Instrumental Variables Regression I In. Figure 8.1 ETS Sample Files Window 2 From the JMP Home window, select SAS I Econometrics and Time Series I Fit Instrumental Variables Regression. The Instrumental Variables Regression initial model window appears. (See Figure 8.2.)

99 Step 1. Specify and Estimate a Base Model in the Initial Model Window 93 Figure 8.2 Example Instrumental Variables Regression Launch Window 3 Specify the Y (response) variable by selecting the variable in the Select Columns list and then clicking Y, Response. 4 (Optional) Specify endogenous explanatory variables by selecting the variables in the Select Columns list and then clicking Endogenous, Explanatory. You can select more than one variable by holding CTRL and clicking on each variable that you want to select. NOTE: The endogenous explanatory variables that you select from the initial model window become the master list of endogenous variables for the subsequent models. You can only select a subset of variables from the master list as endogenous regressors; you cannot add new variables to the master list. 5 (Optional) Specify exogenous explanatory variables by selecting the variables in the Select Columns list and then clicking Exogenous, Explanatory. NOTE: The exogenous explanatory variables that you select from the initial model window become the master list of exogenous variables for the subsequent models. You can only select a subset of variables from the master list as exogenous regressors; you cannot add new variables to the master list. In addition, instrumental variables can come only from this exogenous variables list. 6 Click OK to estimate the model. The base model includes all endogenous and exogenous variables as its regressors.

100 94 Chapter 8: Fit Instrumental Variables Regression Step 2. Examine Base Model Results in the Results Window After you create and estimate the base model, the Instrumental Variables Regression Results window appears. (See Figure 8.3.) Figure 8.3 Example Instrumental Variables Regression Results Window

101 Step 2. Examine Base Model Results in the Results Window 95 The Instrumental Variables Regression Results window contains the following areas: The Data Summary area contains a distribution plot with tables of the quantiles and summary statistics for the observed data. The Fitted Models area is similar for all analyses. For more information, see the section Results Window on page 5. The Model Comparison area is similar for all analyses. For more information, see the section Model Comparison Area on page 8. The Model Estimates area contains the following information: model estimates results: fit statistics and parameter estimates; first-stage regression statistics if estimation method is either two-stage least squares estimation or limited information maximum likelihood estimation instrumental variables regression model graphics: plot of residuals, residual by predicted plot, plot of actual and predicted values, Q-Q plot of residuals, and histogram of residuals for the response variable See Figure 8.4 for an example of the Model Estimates area.

102 96 Chapter 8: Fit Instrumental Variables Regression Figure 8.4 Example Model Estimates Area in the Instrumental Variables Regression Results Window You examine the Instrumental Variables Regression Results window to determine how to modify the base model to create an alternative model that is a better representation of your data. By clicking the red triangles next to headings in the results window, you can modify the view of the plots and tables shown or you can add more plots or tables to the results window. You can also collapse or expand sections by clicking the gray triangles next to the headings in this window.

103 Step 3. Create and Estimate an Alternative Model in the Options Window 97 Step 3. Create and Estimate an Alternative Model in the Options Window 1 In the Instrumental Variables Regression Results window, you can open an Instrumental Variables Regression Options window (see Figure 8.5) to create a new model by doing one of the following: Figure 8.5 Model Tab of the Instrumental Variables Regression Options Window Click the New Model button at the bottom of the Fitted Models area. The Instrumental Variables Regression Options window appears with the current model settings. Click the red triangle next to the Fitted Models heading, and then select New Model. The Instrumental Variables Regression Options window appears with the current model settings. Click the red triangle next to Model 1 in the Fitted Models area, and select one of the following commands:

104 98 Chapter 8: Fit Instrumental Variables Regression Edit opens the Instrumental Variables Regression Options window. This window contains the current model settings. NOTE: If you choose this option and perform the remaining steps, you can no longer compare the base model to any alternative models. Copy creates a copy of the base model. Then click the red triangle next to Copy of Model 1, and select Edit to open the Instrumental Variables Regression Options window. This window contains the values of the copied model. 2 In the Instrumental Variables Regression Options window, specify an alternative model. For more information about this window and its tabs, see the following section. 3 Click OK to estimate the alternative model. The Instrumental Variables Regression Options window closes, and the model results for the alternative model appear in the Instrumental Variables Regression Results window. For more information, see the section Results Window on page 5. Instrumental Variables Regression Options Window The Instrumental Variables Regression Options window contains one model tab. The options on this tab correspond to statements or options in the SAS/ETS SYSLIN procedure. Model Tab On the Model tab, you specify regression model related options. (See Figure 8.5.) Model Variables specify the regressors and instrumental variables in the model. Note that there are two sublists, Exogenous and Endogenous, in the Select Columns list. These two sublists are defined in the Instrumental Variables Regression Launch window (see Figure 8.2). To add a regressor variable to the model: 1 Select the variable in the Select Columns list. You can select more than one variable at a time by holding CTRL and clicking on each variable that you want to add. 2 Click. The variables that you select are moved from the Select Columns list to the Explanatory Variables list. To remove a regressor variable from the model: 1 Select the variable in the Explanatory Variables list. You can select more than one variable at a time by holding CTRL and clicking on each variable that you want to remove. 2 Click. The variables that you select are moved from the Explanatory Variables list to the Select Columns list. Note that the selected variables are placed back under the corresponding Exogenous or Endogenous node in the Select Columns list.

105 Model Settings Window 99 You can also add or remove instrumental variables from the model in the same way as regressor variables. You cannot add an endogenous variable(s) to the Instrumental Variables list. NOTE: You can compare models that contain different explanatory and instrumental variables either by using the overall model fit information (for example, root MSE or the R-square values) for each model or by using the model comparison graph. Estimation Method specifies the estimation method. Select one of the following from the Estimation Method list: Ordinary Least Squares Estimation (this is the default) Two-stage Least Squares Estimation Limited Information Maximum Likelihood Estimation NOTE: When you select two-stage least squares estimation or limited information maximum likelihood estimation and click OK to run the analysis, a warning message window pops up if the number of instrumental variables is less than the number of endogenous regressors. The analysis can be run when you change the model variables until the number of instrumental variables is greater than or equal to the number of endogenous regressors. Settings Windows Fit Instrumental Variables Regression analysis provides three settings windows. The SAS Graphs Settings window and Display Settings window are described in the section Add-in Main Menu on page 11. The Model Settings window is described in the following section. Model Settings Window The Model Settings window, shown in Figure 8.6, currently contains only the option to show or hide the first-stage regression statistics for the endogenous variables regressed on the instruments. Figure 8.6 Model Settings Window

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107 Chapter 9 Fit Unobserved Components Models Contents Overview of Fit Unobserved Components Models Specify an Unobserved Component Model Step 1. Specify and Estimate a Base Model Step 2. Examine Base Model Results in the Results Window Step 3. Create and Estimate an Alternative Model in the Options Window The Unobserved Components Model Options Window Components Tab Regressors Tab The Settings Window Forecast Settings Window Overview of Fit Unobserved Components Models You select Fit Unobserved Components Models to fit unobserved components models. Unobserved components models (UCMs) are used to forecast equally spaced univariate time series data. UCMs are also called structural models in the time series literature. A UCM decomposes the response series into components such as trend, seasonals, cycles, and the regression effects due to predictor series. The components in the model attempt to capture the salient features of the series that are useful in explaining and predicting its behavior. Fit Unobserved Components Models can be used to fit unobserved components models with one or more of the following components: autoregressive seasonal cycle irregular level regression slope

102 Chapter 9: Fit Unobserved Components Models The first part of this chapter describes how to perform a Fit Unobserved Components Models analysis.

108 102 Chapter 9: Fit Unobserved Components Models The first part of this chapter describes how to perform a Fit Unobserved Components Models analysis. The second and third parts provide a detailed description of the windows that are associated with Fit Unobserved Components Models. Specify an Unobserved Component Model Step 1. Specify and Estimate a Base Model The base model for Fit Unobserved Components Models includes level, seasonal, and slope components. To specify and estimate a base model: 1 Open a data file. From the JMP Home window, select SAS I Econometrics and Time Series I ETS Sample Data. The ETS Sample Files window appears. (See Figure 9.1.) Select Unobserved Components Models I seriesg. Figure 9.1 ETS Sample Files Window 2 From the JMP Home window, select SAS I Econometrics and Time Series I Fit Unobserved Components Models. The Unobserved Components Model initial model window appears. See Figure 9.2.

109 Step 2. Examine Base Model Results in the Results Window. 103 Figure 9.2 Example Initial Model Window for Fit Unobserved Component Model 3 Specify the Y (response) variable by selecting the variable in the Select Columns list and then clicking Y, Response. 4 (Optional) Specify any X (explanatory) variables by selecting the variables in the Select Columns list and then clicking X, Explanatory. You can select more than one variable by holding CTRL and clicking on each variable that you want to add. 5 (Optional) Specify the Z (ID) variable by selecting the variable in the Select Columns list and then clicking Z, ID. 6 (Optional) Specify an interval for the observations by selecting a value from the Interval list. 7 Click OK to estimate the model. Step 2. Examine Base Model Results in the Results Window. After you create the base model, the Unobserved Components Model Results window appears. (See Figure 9.3.)

110 104 Chapter 9: Fit Unobserved Components Models Figure 9.3 Example Unobserved Components Models Results Window

111 Step 2. Examine Base Model Results in the Results Window. 105 The Unobserved Components Model Results window contains the following areas: The Data Summary area contains the original data in an X Y plot and a distribution plot with tables of the quantiles and summary statistics for the observed data. The Fitted Models area is similar for all analyses. For more information, see the section Fitted Models Area on page 6. The Model Comparison area is similar for all analyses. For more information, see the section Model Comparison Area on page 8. The Model Estimates area of the results window contains the following information: parameter estimates estimation span goodness-of-fit statistics residual distribution information outlier summary additional results UCM model graphics UCM model forecast UCM model forecast data table See Figure 9.4 and Figure 9.5 for examples of the Model Estimates area of the Unobserved Components Model Results window.

112 106 Chapter 9: Fit Unobserved Components Models Figure 9.4 Example Model Estimates Area in a Unobserved Components Model Results Window

113 Step 2. Examine Base Model Results in the Results Window. 107 Figure 9.5 Example Model Estimates Area in a Unobserved Components Model Results Window Continued You examine the Unobserved Components Model Results window to determine how to modify the base model to create an alternative model that is a better representation of your data. You can modify the plots and tables shown by clicking the red triangles next to headings in the results window. You can also collapse or expand sections by clicking the gray triangles next to the headings in this window.

114 108 Chapter 9: Fit Unobserved Components Models Step 3. Create and Estimate an Alternative Model in the Options Window 1 In the Unobserved Components Model Results window, you can open a Unobserved Components Model Options window (see Figure 9.6) to create a new model by doing one of the following: Figure 9.6 Example Unobserved Components Model Options Window Click the New Model button at the bottom of the Fitted Models area. The Unobserved Components Model Options window appears with the current model settings. Click the red triangle next to the Fitted Models heading, and then select New Model. The Unobserved Components Model Options window appears with the current model settings. Click the red triangle next to Model 1 in the Fitted Models area, and select one of the following commands:

115 Components Tab 109 Edit opens the Unobserved Components Model Options window. This window contains the current model settings. NOTE: If you choose this option and perform the remaining steps, you can no longer compare the base model to any alternative models. Copy creates a copy of the base model. Then click the red triangle next to Copy of Model 1, and select Edit to open the Unobserved Components Model Options window. This window contains the values for the copied model. 2 In the Unobserved Components Model Options window, specify an alternative model. For more information about this window and its tabs, see the following section. 3 Click OK to estimate the alternative model. The Unobserved Components Model Options window closes, and the model results for the alternative model appear in the Unobserved Components Model Results window. For more information, see the section Results Window on page 5. The Unobserved Components Model Options Window The Unobserved Components Model Options window contains two tabs, which are described in the following sections. Options on these tabs correspond to options or statements for the SAS/ETS UCM procedure. Components Tab On the Components tab, you specify which components to use in an unobserved component model. Figure 9.6 shows an example of the Components tab. By default, the Components tab includes level, seasonal, and slope components, but you can add or remove components. To add a component, select the component from the All UCM Components list and then click. To remove a component, select the component from the Components to be used list and then click. If you click a component in the Components to be used area, a description and the required options for the selected component appear in the Options area. To specify optional options, click Show advanced to show the Advanced Options area. Now the Show advanced button changes to Hide advanced. You can click Hide advanced to hide the Advanced Options area. See Figure 9.7 for an example of the Advanced Options area of the component Season 1. Figure 9.7 Example Advanced Options Area

116 110 Chapter 9: Fit Unobserved Components Models Specify any options you want in the Advanced Options area. The following sections describe the options associated with each component. Options for a Level Component When you select Level from the Components to be used list, there are no required options. You can specify the following options, which correspond to options in the LEVEL statement of the UCM procedure: Disturbance variance specifies an initial value for the disturbance variance during the parameter estimation process. Any nonnegative value, including 0, is an acceptable starting value. This option corresponds to the VARIANCE= option. Fix variance value specifies whether to fix the disturbance to the value specified in the Disturbance variance option. This option corresponds to the NOEST option. Check breaks specifies whether to check for breaks in the level component. This option corresponds to the CHECK- BREAK option. Options for a Season 1 or Season 2 Component When you select Season 1 or Season 2 from the Components to be used list, you can also specify values for the following required options (these options correspond to options in the SEASON statement of the UCM procedure): Seasonal length specifies the season length. The season length can be any integer greater than or equal to 2. Typical examples of season lengths are 12, which corresponds to monthly seasonality, and 4, which corresponds to quarterly seasonality. This option corresponds to the LENGTH= option. Seasonal Type specifies the type of the seasonal component. The default type is DUMMY. This option corresponds to the TYPE= option. Click Show advanced to specify the following options in the Advanced Options area (these options correspond to options in the SEASON statement of the UCM procedure): Disturbance variance specifies an initial value for the disturbance variance during the parameter estimation process. Any nonnegative value, including 0, is an acceptable starting value. This option corresponds to the VARIANCE= option. Fix variance value specifies whether to fix the disturbance to the value specified in the Disturbance variance option. This option corresponds to the NOEST=VARIANCE option.

117 Components Tab 111 Options for a Slope Component When you select Slope from the Components to be used list, there are no required options. You can specify the following options, which correspond to options in the SLOPE statement of the UCM procedure: Disturbance variance specifies an initial value for the disturbance variance during the parameter estimation process. Any nonnegative value, including 0, is an acceptable starting value. This option corresponds to the VARIANCE= option. Fix variance value specifies whether to fix the disturbance to the value specified in the Disturbance variance option. This option corresponds to the NOEST=VARIANCE option. Options for an Autoregression Component When you select Autoregression from the Components to be used list, there are no required options. You can specify the following options, which correspond to options in the AUTOREG statement of the UCM procedure: Damping factor RHO specifies an initial value for the damping factor during the parameter estimation process. The value of must be in the interval Œ 1; 1/ (which includes 1, but excludes 1). This option corresponds to the RHO= option. Fix damping value specifies whether to fix the to the value specified in the Damping factor RHO option. This option corresponds to the NOEST=RHO option. Disturbance variance specifies an initial value for the disturbance variance during the parameter estimation process. Any nonnegative value, including 0, is an acceptable starting value. This option corresponds to the VARIANCE= option. Fix variance value specifies whether to fix the disturbance to the value specified in the Disturbance variance option. This option corresponds to the NOEST=VARIANCE option. Options for an Irregular Error Component When you select Irregular Error from the Components to be used list, there are no required options. You can specify the following options, which correspond to options in the IRREGULAR statement of the UCM procedure: Error variance specifies an initial value for the disturbance variance during the parameter estimation process. Any nonnegative value, including 0, is an acceptable starting value. This option corresponds to the VARIANCE= option.

118 112 Chapter 9: Fit Unobserved Components Models Fix variance value specifies whether to fix the disturbance to the value specified in the Error variance option. This option corresponds to the NOEST option. ARMA Specification specifies options for an ARMA model for the irregular component: p sp q sq s specifies the order of the nonseasonal autoregressive polynomial. The order can be any nonnegative integer; the default value is 0. In practice, the order is a small integer such as 1, 2, or 3. This option corresponds to the P= option. specifies the order of the seasonal autoregressive polynomial. The order can be any nonnegative integer; the default value is 0. In practice, the order is a small integer such as 1 or 2. This option corresponds to the SP= option. specifies the order of the nonseasonal moving average polynomial. The order can be any nonnegative integer; the default value is 0. In practice, the order is a small integer such as 1, 2, or 3. This option corresponds to the Q= option. specifies the order of the seasonal moving average polynomial. The order can be any nonnegative integer; the default value is 0. In practice, the order is a small integer such as 1 or 2. This option corresponds to the SQ= option. specifies the season length used during the specification of the seasonal autoregressive or seasonal moving average polynomial. The season length can be any positive integer; for example, S=4 might be an appropriate value for a quarterly series. The default value is S=1. This option corresponds to the S= option. Options for a Block Season Component When you select Block Season from the Components to be used list, you can also specify values for the following required options (these options correspond to options in the BLOCKSEASON statement of the UCM procedure): Block Size specifies the block size. The block size can be any integer larger than or equal to 2. Typical examples of block sizes are 24 (which corresponds to the hours of the day when a day is used as a block in hourly data), or 60 (which corresponds to the minutes in an hour when an hour is used as a block in data that are recorded by minutes). This option corresponds to the BLOCKSIZE= option. Number of Blocks specifies the number of blocks. The number of blocks can be any integer greater than or equal to 2. This option corresponds to the NBLOCKS= option. Click Show advanced to specify the following options in the Advanced Options area (these options correspond to options in the BLOCKSEASON statement of the UCM procedure):

119 Components Tab 113 Position of the first measurement specifies the position of the first measurement within the block, if the first measurement is not at the start of a block. The value must be between 1 and the block size. The default value is 1. The first measurement refers to the start of the estimation span and the forecast span. If these spans differ, their starting measurements must be separated by an integer multiple of the block size. This option corresponds to the OFFSET= option. Block Season Type specifies the type of the block seasonal component. The default type is DUMMY. This option corresponds to the TYPE= option. Disturbance variance specifies an initial value for the disturbance variance during the parameter estimation process. Any nonnegative value, including 0, is an acceptable starting value. This option corresponds to the VARIANCE= option. Fix variance value specifies whether to fix the disturbance to the value specified in the Disturbance variance option. This option corresponds to the NOEST option. Options for a Cycle 1, Cycle 2, or Cycle 3 Component When you select Cycle 1, Cycle 2, or Cycle 3 from the Components to be used list, you can also specify values for the following required options (these options correspond to options in the CYCLE statement of the UCM procedure): Cycle period specifies an initial value for the cycle period during the parameter estimation process. The value must be strictly greater than 2. This option corresponds to the PERIOD= option. Fix period value specifies whether to fix the cycle period values to those specified in the Cycle period option. This option corresponds to the NOEST=PERIOD option. Damping factor RHO specifies an initial value for the damping factor during the parameter estimation process. The value of must be in the interval Œ 1; 1/ (which includes 1, but excludes 1). This option corresponds to the RHO= option. Fix damping value specifies whether to fix the damping factor to the value specified in the Damping factor RHO option. This option corresponds to the NOEST=RHO option. Disturbance variance specifies an initial value for the disturbance variance during the parameter estimation process. Any nonnegative value, including 0, is an acceptable starting value. This option corresponds to the VARIANCE= option. Fix variance value specifies whether to fix the disturbance to the value specified in the Disturbance variance option. This option corresponds to the NOEST=VARIANCE option.

120 114 Chapter 9: Fit Unobserved Components Models Options for a Lagged Dependent Variable Component When you select Lagged Dependent Variable from the Components to be used list, there are no required options. You can specify the following options, which correspond to options in the DEPLAG statement of the UCM procedure: Lags specify the lags of the dependent variable to be included as predictors in the model. This option corresponds to the LAGS= option. PHI lists starting values for the coefficients of the lagged dependent variable. The order of the values listed corresponds with the order of the lags specified in the Lags option. This option corresponds to the PHI= option. Fix phi value specifies whether to fix the coefficients to the values specified in PHI option. This option corresponds to the NOEST option. Options for a Random Regression Component When you select Random Regression from the Components to be used list, there are no required options. You can add or remove regressors with time-varying regression coefficients. Figure 9.8 shows an example of the Random Regression options area. Figure 9.8 Example Random Regression Options Area To add a Regressor (Z) variable to the model: 1 Select the variable in the Select Columns list. You can select more than one variable at a time by holding CTRL and clicking on each variable that you want to add. 2 Click. The variables that you select are moved from the Select Columns list to the Explanatory Variables list.

121 Components Tab 115 To remove a Regressor (Z) variable from the model: 1 Select the variable in the Explanatory Variables list. You can select more than one variable at a time by holding CTRL and clicking on each variable that you want to remove. 2 Click. The variables that you select are moved from the Explanatory Variables list to the Select Columns list. The following options (which correspond to options in the RANDOMREG statement of the UCM procedure) are available in the Random Regression Options area: Disturbance variance specifies an initial value for the disturbance variance during the parameter estimation process. Any nonnegative value, including 0, is an acceptable starting value. This option corresponds to the VARIANCE= option. Fix variance specifies whether to fix the disturbance to the value specified in the Disturbance variance option. This option corresponds to the NOEST option. Options for a Spline Regression Component When you select Spline Regression from the Components to be used list, there are no required options. You can add or remove regressors that have a nonlinear relationship with the outcome variable that can be approximated by a given B-spline. These options correspond to the options in the SPLINEREG statement of the UCM procedure. To add a Regressor (Z) variable to the model: 1 Select the variable in the Select Columns list. You can select more than one variable at a time by holding CTRL and clicking on each variable that you want to add. 2 Click. The variables that you select are moved from the Select Columns list to the Explanatory Variables list. To remove a Regressor (Z) variable from the model: 1 Select the variable in the Explanatory Variables list. You can select more than one variable at a time by holding CTRL and clicking on each variable that you want to remove. 2 Click. The variables that you select are moved from the Explanatory Variables list to the Select Columns list. The following options (which correspond to options in the SPLINEREG statement of the UCM procedure) are available in the Spline Regression options area:

122 116 Chapter 9: Fit Unobserved Components Models Degree of the spline specifies the degree of the spline, n. n can be any integer greater than or equal to 0. The default value is 3. The polynomial degree should be a small integer, usually 0, 1, 2, or 3. Larger values are rarely useful. If you have any doubt as to what degree to specify, use the default. This option corresponds to the DEGREE= option. Disturbance variance specifies an initial value for the disturbance variance during the parameter estimation process. Any nonnegative value, including 0, is an acceptable starting value. This option corresponds to the VARIANCE= option. Fix variance specifies whether to fix the disturbance to the value specified in the Disturbance variance option. This option corresponds to the NOEST option. Knots specifies the interior knots or break points. The values in the knot list must be nondecreasing and must lie between the minimum and the maximum of the spline regressor values in the input data set. The first time you specify a value in the knot list, it indicates a discontinuity in the nth (from the degree of the spline option) derivative of the transformation function at the value of the knot. The second mention of a value indicates a discontinuity in the (n 1)th derivative of the transformation function at the value of the knot. Knots can be repeated any number of times for decreasing smoothness at the break points, but the values in the knot list can never decrease. This option corresponds to the KNOTS= option. Options for a Spline Season Component When you select Spline Season from the Components to be used list, you can also specify values for the following required options (these options correspond to options in the SPLINESEASON statement of the UCM procedure): Seasonal length specifies the season length. The season length can be any integer greater than or equal to 2. Typical examples of season lengths are 12 (which corresponds to monthly seasonality), or 4 (which corresponds to quarterly seasonality). This option corresponds to the LENGTH= option. Click Show advanced to specify the following options in the Advanced Options area (these options correspond to options in the SPLINESEASON statement of the UCM procedure): Degree of the spline specifies the degree of the spline. The value can be any integer greater than or equal to 0. The default value is 3. The polynomial degree should be a small integer, usually 0, 1, 2, or 3. Larger values are rarely useful. If you have any doubt as to what degree to specify, use the default. This option corresponds to the DEGREE= option. Position of the first measurement offset specifies the position of the first measurement within the season, if the first measurement is not at the start of the season. The value must be between 1 and the season length. The default is 1. The

123 Regressors Tab 117 first measurement refers to the start of the estimation span and the forecast span. If these spans differ, their starting measurements must be separated by an integer multiple of the season length. This option corresponds to the OFFSET= option. Disturbance variance specifies an initial value for the disturbance variance during the parameter estimation process. Any nonnegative value, including 0, is an acceptable starting value. This option corresponds to the VARIANCE= option. Fix variance value specifies whether to fix the disturbance to the value specified in the Disturbance variance option. This option corresponds to the NOEST option. Knots lists the internal knots. This list of values must be a nondecreasing sequence of integers within the range of 2 to s 1, where s is the season length specified in the Seasonal Length option. This option corresponds to the KNOTS= option. Regressors Tab On the Regressors tab, you specify the X (explanatory) variables, which are sometimes referred to as regressor variables. An example of the Regressors tab is shown in Figure 9.9. To add a regressor variable to the model: 1 Select the variable in the Select Columns list. You can select more than one variable at a time by holding CTRL and clicking on each variable that you want to add. 2 Click. The variables that you select are moved from the Select Columns list to the Explanatory Variables list. To remove a regressor variable from the model: 1 Select the variable in the Explanatory Variables list. You can select more than one variable at a time by holding CTRL and clicking on each variable that you want to remove. 2 Click. The variables that you select are moved from the Explanatory Variables list to the Select Columns list. NOTE: Models with different X variables can be compared, either by using the fitted or residual graphs or by using the overall model fit information (for example, AIC or BIC) for each model.

124 118 Chapter 9: Fit Unobserved Components Models Figure 9.9 Unobserved Components Model Options Window with the Regressors Tab The Settings Window Fit Unobserved Components Models analysis provides three settings windows: Forecast Settings, SAS Graphs Settings, and Display Settings. The SAS Graphs Settings window is described in the section SAS Graphs Settings Window on page 11. The Display Settings window is described in the section Display Settings Window on page 12. The Forecast Settings window is described in the following section.

Forecast Settings Window 119 Forecast Settings Window In the Forecast Settings window, you specify the forecast and outlier options. Figure 9.10 shows an example of the Forecast Settings window.

125 Forecast Settings Window 119 Forecast Settings Window In the Forecast Settings window, you specify the forecast and outlier options. Figure 9.10 shows an example of the Forecast Settings window. Figure 9.10 Forecast Settings Window for Fit Unobserved Components Models The Forecast Settings window contains the following options which correspond to options in the FORECAST and OUTLIER statements of the UCM procedure: Produce Forecasts specifies the overall forecasting environment for the specified model. This option corresponds to including the FORECAST statement in the UCM procedure. When you select this check box, you can also specify the following options, which correspond to options in the FORECAST statement of the UCM procedure: Lead= specifies the number of periods to forecast beyond the historical period defined by the Skip First

126 120 Chapter 9: Fit Unobserved Components Models and Skip Last options. For example, entering 10 in the Lead area results in the forecasting of 10 future values of the response series. The default is 12. This option corresponds to the LEAD= option. Skip First and Skip Last specify the holdout sample for the evaluation of the forecasting performance of the model. For example, specifying 10 in the Skip Last area results in treating the last 10 observed values of the response series as unobserved. A post-sample prediction analysis table is produced for comparing the predicted values with the actual values in the holdout period. The default is 0. These options correspond to the SKIPLAST= and SKIPFIRST= options, respectively. Alpha= specifies the significance level of the forecast confidence intervals. For example, ALPHA=0.05, which is the default, results in a 95% confidence interval. Specify Outlier Options enables you to control the reporting of the additive outliers (AO) and level shifts (LS) in the response series. The AOs are searched by default. This option corresponds to including the OUTLIER statement in the UCM procedure. When you select this check box, you can also specify the following options, which correspond to options in OUTLIER statement of the UCM procedure: Alpha= specifies the significance level for reporting outliers. The default is 0.05, which results in a 95% confidence interval. This option corresponds to the ALPHA= option. Max Number of Outliers limits the number of outliers to search. The default is 5. This option corresponds to the MAXNUM= option. Max Percentage of Outliers limits the number of outliers to search. The default is 1. This option corresponds to the MAXPCT= option.

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131 SAS Publishing Delivers! Whether you are new to the work force or an experienced professional, you need to distinguish yourself in this rapidly changing and competitive job market. SAS Publishing provides you with a wide range of resources to help you set yourself apart. Visit us online at support.sas.com/bookstore. SAS Press Need to learn the basics? Struggling with a programming problem? You ll find the expert answers that you need in example-rich books from SAS Press. Written by experienced SAS professionals from around the world, SAS Press books deliver real-world insights on a broad range of topics for all skill levels. SAS Documentation support.sas.com/saspress To successfully implement applications using SAS software, companies in every industry and on every continent all turn to the one source for accurate, timely, and reliable information: SAS documentation. We currently produce the following types of reference documentation to improve your work experience: Online help that is built into the software. Tutorials that are integrated into the product. Reference documentation delivered in HTML and PDF free on the Web. Hard-copy books. support.sas.com/publishing SAS Publishing News Subscribe to SAS Publishing News to receive up-to-date information about all new SAS titles, author podcasts, and new Web site features via . Complete instructions on how to subscribe, as well as access to past issues, are available at our Web site. support.sas.com/spn SAS and all other SAS Institute Inc. product or service names are registered trademarks or trademarks of SAS Institute Inc. in the USA and other countries. indicates USA registration. Other brand and product names are trademarks of their respective companies SAS Institute Inc. All rights reserved _1US.0109

SAS Econometrics and Time Series Analysis 1.1 for JMP

SAS Econometrics and Time Series Analysis 1.1 for JMP SAS Documentation The correct bibliographic citation for this manual is as follows: SAS Institute Inc. 2011. SAS Econometrics and Time Series Analysis