STAMP 5.0: A Review. Francis X. Diebold, Lorenzo Giorgianni, and Atsushi Inoue

Transcription

1 STAMP 5.0: A Review Francis X. Diebold, Lorenzo Giorgianni, and Atsushi Inoue Department of Economics University of Pennsylvania 3718 Locust Walk Philadelphia, PA February 1996 Acknowledgments: We thank the National Science Foundation, the Sloan Foundation and the University of Pennsylvania Research Foundation for

2 support. STAMP -- Structural Time Series Analyser, Modeller and Predictor. STAMP, version 5.0, Chapman and Hall, 2-6 Boundary Row, Freepost (SN- 927), London SE1 8BR. Single-user list price 500; academic discounts -1- available. Package consists of a 382-page manual (Koopman et al., 1995) and two 3.5 inch 1.44 M diskettes. Requires: (1) IBM PC or compatible running DOS 3.3 or higher, (2) 460K of free memory for the DOS version and 100K of free memory and 1.2M of free extended memory for the 386 version, (3) 3M free hard disk space, and (4) Hercules, CGA, MCGA, EGA, VGA, or Super VGA video card. 1. Introduction and Overview Having reviewed an earlier version of STAMP (Diebold, 1989) and the underlying statistical theory (Diebold, 1992), it s a pleasure to continue the tradition with a review of STAMP version 5.0. STAMP (Structural Time Series Analyser, Modeller and Predictor) provides tools for modeling and forecasting time series using unobserved component (UC) models, in which observed time series are assumed to be additively composed of unobserved trend, seasonal, cyclical and irregular components. More specifically, the software implements

3 -2- the framework of Harvey (1989) and Harvey and Shephard (1993), which of course builds on earlier work such as Nerlove et al. (1979). The software is easy to use -- STAMP is menu-driven and small enough such that its structure can be fully understood after only a few hours of exploration. At the top of the screen, the expected menus such as "File," "Edit," "Data," "Model," "Test," "Options," "Window," and "Help" pop down with a click of the mouse, and from there one can access any of the available procedures. STAMP s ease of use certainly should not be confused with lack of power or sophistication. On the contrary, STAMP 5.0 really shines on what counts most -- modern, best-practice time-series and forecasting techniques. For example: (1) The theory and algorithms underlying STAMP 5.0 are state-of-the-art. Throughout, maximum likelihood estimates of (typically nonstationary) models are obtained using the Kalman Filter with diffuse initial conditions. Iteration begins with the EM algorithm, to get close to the likelihood optimum, and then switches to a quasi-newton algorithm in light of the slow convergence rate of EM. (2) The new multivariate capabilities of STAMP 5.0 are impressive and their

4 -3- integration seamless. Common features across series (trends, seasonals or cycles) can be immediately incorporated by imposing a reduced-rank structure on the component shock matrices. (3) STAMP 5.0 is newly rewritten in C and shares the same data management and graphical interface with the PcGive and PcFiml programs. (See Doornik and Hendry, 1994a, 1994b.) In what follows we review STAMP s manual (Section 2), data management capabilities (Section 3), and modeling and testing capabilities (Section 4). Finally, we offer some complaints about the present version and suggestions for the next (Section 5). 2. Working through the manual The manual consists of six parts: (1) Prologue, (2) Tutorials on structural time series modeling, (3) STAMP tutorials, (4) Statistical output, (5) STAMP manuals, and (6) Appendices. Parts (1)-(3) give an overview of the program s capabilities and constitute a user s guide, while parts (4)-(6) give more detailed descriptions of the components of the program and constitute a reference manual. Part 1 (Prologue)

5 -4- Part 1 explains installation procedures and program basics. It also describes a variety of interesting tutorial data sets, most of which have appeared in published studies, including the well-known airline passenger data, plus other useful economic and non-economic data, such as daily exchange rates for the US dollar, US and UK macroeconomic time series, rainfall in north-east Brazil, road casualties in the UK, etc. Part 2 (Tutorials on structural time series modeling) Part 2 explains how to use STAMP to build and estimate univariate and multivariate unobserved component models, possibly incorporating intervention and/or explanatory variables. In the multivariate case, it discusses how to use STAMP to model common trends, common cycles, common factors, and common seasonals, as well as to perform seasonal adjustment and detrending. Finally, it walks the reader through an instructive sequence of interesting economic and financial applications of UC models, which allow one to learn STAMP while replicating the results of several existing empirical studies. Part 3 (STAMP tutorials) Part 3 provides detailed tutorials on data management, graphics, modeling, testing, and forecasting. Given that some of the procedures and commands here described are shared by PcGive/PcFiml, a large section of this

6 -5- part of the manual parallels Doornik and Hendry (1994a, 1994b) and its reading may result redundant to an expert user of PcGive/PcFiml. However, Chapter 12 is not to be missed. This chapter provides an overview of UC model specification, estimation, testing and forecasting. Part 4 (Statistical output) Part 4 explains in detail the statistical methods that underlie STAMP. It summarizes the theoretical background of state space modeling and the Kalman filter, including recent developments such as the proper treatment of diffuse initial conditions in nonstationary models. It also provides exact definitions of the descriptive statistics and of other statistical output. Part 5 (STAMP manuals) Part 5 is divided into three chapters. Each chapter provides detailed description of subjects such as: data file format and compatibility for import/export purposes, technical requirements and limitations for memory and graphics, treatment of missing values, available algebraic functions, etc. This part concludes with a synthetic description of each menu s commands. Part 6 (Appendices) Part 6 contains technical appendices describing various add-ons shipped with STAMP (e.g., utilities for printing ASCII files and graphs, or for

7 -6- modifying the base configuration) and an explanatory list of common error messages. It also contains a description of the DOS extender, a utility which allows STAMP to use memory (RAM) up to 4GB or to manage a hard disk swap file. This part of the manual also draws extensively from Doornik and Hendry (1994a, 1994b). 3. Data Management The data management and the graphical interfaces are shared with the PcGive and PcFiml programs (Doornik and Hendry, 1994a, 1994b). There are two menus relevant to data management: the file and the data menus. The File Menu In the file menu, the following options are available: "load data", "append data", "save data", "open results", "save results as", "view a file", "view a PCX file", "operating shell", and "exit". The first three commands and the last command do not need explanation. The load data command reads and imports PcGive 7 data files, ASCII files, and Excel & Lotus spreadsheets. STAMP supports up to 500 variables with 50,000 observations when stamp.exe (the 386 version of the program) is

8 -7- executed. The commands executed during a STAMP session and the statistical output generated are conveniently written in a result window, which can be stored in a disk file with the command save results as. This feature is particularly useful because it allows recording of a working session as it develops in time, and permits adding notes and comments to the statistical results on the fly. With the command "open results", STAMP gives the option of opening previously existing result files. The "view a file" command reads ASCII files, and the "view a PCX file" command allows viewing and editing previously saved graphs. The "operating shell" command opens a DOS shell. The Data Menu The "data" menu contains a second set of data management commands. The following commands are available through this menu: "graph," "transform," "view/edit database," "create a new variable," "calculator," "algebra," and "tail probability". The "graph" command can simultaneously display up to 16 different plots and 36 variables on one screen. Graphs can be edited with the addition of text and lines, or saved (to be imported in popular wordprocessors, or re-viewed at a later stage). In addition to time plots, the "graph" command can draw scatter plots and add regression lines. The

9 -8- transform dialog transforms variables currently stored in the data file: such transformations include logarithmic, exponential, absolute value, differencing and integration (including seasonal differencing and integration). In addition, this menu offers the possibility of detrending variables using the Hodrick- Prescott filter and of implementing a Taylor series expansion of the type often encountered in the estimation of stochastic volatility models (see p. 85 of Koopman et al., 1995). The "describe" option, within the transform dialog box, provides graphical descriptive statistics of the (transformed or untransformed) data, including correlograms, periodograms, estimated spectra, histograms, nonparametric density estimates, cumulative distribution function estimates, etc. Summary statistics such as means, standard deviations, etc., can be produced easily by selecting the "write report" option within the describe sub-menu. Marginal significance values are conveniently produced along with the values of the statistics. By choosing the "view/edit database" command, a database spreadsheetlike window pops up. Within this window, it is possible to edit the data, or, by clicking with the mouse on a variable header, it is possible to access the data documentation editor window, where comments and descriptors to variable

10 -9- names can be attached. The "calculator" option mimics a pocket calculator, with which one can transform existing series and attach them to the database. The "algebra" option transforms data by mathematical formulae written in the algebra editor. The code written in the "algebra editor" can be saved, reloaded, and executed again (note that it is possible, by shelling to DOS and then re-entering the program, to use external editors for the purpose of constructing algebra codes). The "tail probability" command gives the p-values of several distributions such as (F, t, chi-square, and standard normal distributions.) A few comments on the data management capabilities of STAMP follow. In general, the data management is very efficient, and learning its main features is easy, especially if one has worked before with PcGive/PcFiml. Yet, there are some rigidities of which one must be aware: (1) To be able to append two different data sets, one should make sure, when loading new data using the human readable option (ASCII file format), or when saving data, that the sample end-periods have been defined coherently among existing (PcGive 7) data files. For example, if the data file Prices is defined to go from 80.1 to 95.4 and the data file Quantity is defined to go from to (notice the use here of four digits instead of two to

11 -10- identify the year in the quantity data file), the program would not recognize that the two data sets have the same sample periods, and hence it would fail to append one data set to the other. (2) Renaming PcGive 7 data files (STAMP s default type), by using the DOS ren command makes the data inaccessible for future work. This is because PcGive 7 data is stored in two files, a.bn7 file, which records in binary format the actual data values, and a.in7 (ASCII) file, which stores information about the data set, like sample end-points, frequency and name of the file. If this is changed with the DOS ren command, the header of the data set contained in the information file must be modified as well, to reflect the new data file name and to prevent STAMP from denying access to the renamed data files. 4. Modeling and Testing In the basic (univariate and multivariate) UC model, data are expressed as the sum of different components: trend, seasonal, cycle and irregular. STAMP 5.0 is capable of modeling and estimating even larger models, such as models that include exogenous explanatory variables, lagged values of the dependent variables, AR(1) components and intervention variables. The design and

12 -11- estimation of UC models is carried out in STAMP by accessing the model menu. A variety of routines to validate the performance of the estimated specification are also available in STAMP and are grouped under the test menu. The Model Menu In the "model" menu, the following options are available: "formulate", "components", "interventions", "equation restrictions", "covariance restrictions", "estimation", and "parameter control". These sub-menus are organized in the order in which they would be typically accessed during a model specification and estimation process. The "formulate" sub-menu is the first step of the model-building process: it specifies the variables to be included in the model, assigns the dependent variables and the exogenous variables, including lagged dependent and exogenous variables. When done with this stage, the program brings up the "component" sub-menu, which specifies the unobserved components to be estimated. At this stage one can choose from among an ample set of specifications: from a simple local trend plus irregular model, to a local linear trend model with stochastic seasonals with cyclical and irregular components. From this menu, an "interventions" sub-menu can be accessed to construct three types of intervention variables (dummies): impulse/irregular,

13 -12- level/step, and slope/staircase. If the specified model is multivariate, one can further access the "equation restriction" and the "covariance restrictions" options. The former performs exclusion restrictions on some of the explanatory or intervention variables in any equation of the system. The latter allows one to model common features across series, such as common trends, seasonals or cycles, by imposing reduced rank restrictions on the component shock matrices. Once the model is specified, the "estimation" menu initializes the program s non-linear optimization routine which yields maximum likelihood parameter estimates. Two different estimation strategies are followed for univariate and multivariate models. In both cases, the model is cast in state space form and the likelihood function is computed via the one-step ahead prediction errors delivered by the Kalman filter. For univariate models, the concentrated diffuse log-likelihood function, an unconstrained non-linear function of the parameter space, is maximized by invoking a non-linear quasi- Newton optimization routine. For multivariate models, the estimation strategy is similar, except that the EM algorithm is adopted in a first stage to obtain initial values for the elements of the covariance matrices of the disturbances. Both procedures are described at length in Chapter 14 of Koopman et al. (1995).

14 -13- The "estimation" menu allows control of convergence criteria, the maximum number of iterations and the estimation sample period. Additional control of the estimation/optimization process can be gained by accessing the parameter control sub-menu. This sub-menu permits initialization of optimization routine initial values, restrictions on parameters, and production of a two-dimensional grid plot of the surface of the log-likelihood function against each parameter of the model. When trying to achieve convergence of the optimization procedure for multivariate UC models (often a notoriously slow procedure), or when interpreting the estimation results of estimated UC models with nearly flat loglikelihood functions around maximized values, this option is very useful. After the model is estimated, an "estimation report" and a "diagnostic summary report" are provided. These reports give information about convergence (i.e., strong or weak convergence), the maximized value of the loglikelihood function, the prediction error variance and a set of summary statistics for the estimated residuals, such as a normality test, the Box-Ljung and Durbin- Watson tests for absence of serial correlation and a test for the absence of heteroskedasticity. The marginal significance levels for these statistics are not shown, which is odd given that the marginal significance levels are reported in the transform - describe menu.

15 -14- The Test Menu The test menu is the core of STAMP s abilities in model validation and forecast evaluation. In this menu the following commands are available: "hyperparameters," "final state," "components, joint components," "residual auxiliary residuals," "predictive testing," "forecast," and "forecast editor." For the univariate models, the "hyperparameters" command produces the standard deviations of the estimated disturbances together with frequencies and damping factors for cycles and coefficients for autoregressive components. For multivariate models, it gives the covariance and factor loading matrices of the estimated disturbance vector. The estimate of the final state vector is obtained with the final state command, which produces the latest information on the components in the model. This information is used as input by STAMP at the forecasting stage At this stage, t-values of the single components are produced together with the significance tests of single components (seasonals, cycles and intervention variables, when present) and goodness of fit tests (prediction error variance and mean deviation, coefficients of determination, AIC and BIC information criteria). The "component" and joint components (only for multivariate models) options implement signal extraction. Both graphic and written output can be

16 -15- generated from these commands. For example, after estimating a univariate trend with cycle and seasonal model with the components option one is able to plot the original time series along with its fitted trend line, or the original series with its de-seasonalized counterpart (the trend and cycle); or, in a multivariate model, with the joint components option, one can plot in a pairwise fashion the single series trend or cyclical or seasonal components for detection of common features and lead-lag relationships. Both filtered and smoothed series can be obtained. The "residuals", "auxiliary residual", and "predictive testing" options provide graphical diagnostic checking of the model. They provide correlograms, spectra, CUSUM s and CUSUMSQ s and densities. The auxilliary residual and predictive testing options are useful when one wants to detect and distinguish between outliers and structural breaks. Many diagnostics and predictive failure tests are produced at this stage. The forecast and forecast editor options complete the test menu. Forecasts of the series and of the single components can be produced at this stage, together with many forecast-evaluation statistics. The output generated is mainly graphical and its interpretation aided by addition of pointwise forecast error bounds. Very conveniently, bias-adjusted anti-logarithmic predictions are

17 -16- available for models estimated in logarithms. 5. What Next? Now let us offer some complaints about STAMP 5.0 and suggestions for the next version. (1) If STAMP 5.0 is strong on brains, it is also poor on looks. Throughout, the software and manual have a late 1980s look and feel. For example, the manual notes that a math co-processor is not required but is strongly advised (time to spring for that math co-processor!) and that the program can be run from floppy disks but recommends against it (!), etc., etc. More importantly, significant parts of the manual -- and the user s time -- are devoted to now-arcane patch-ups needed to accomplish routine tasks. STAMP s DOS-based environment can t compete with modern productivityenhancing Windows environments such as E-views (time-series), Stata (crosssection), S+ (general statistics) and Matlab (general technical computing). We look forward to a Windows version of STAMP. (2) One interesting feature of previous versions of STAMP was the use of the frequency-domain asymptotic Gaussian likelihood. Unfortunately, the option of frequency-domain maximum likelihood, whether as an end in itself or

18 -17- as an input to exact time-domain maximum likelihood, appears missing from STAMP 5.0. The frequency-domain calculations are fast and accurate and are therefore useful for the numerically intensive calculations associated with cutting-edge models. Fast computing, moreover, will not reduce the need for fast algorithms for estimating complex models -- as our computational ability grows, so too does the complexity of the models we use, as shown in Koenker (1988). The exact time-domain likelihood calculations for multivariate unobserved-components models, for example, can be quite slow in STAMP 5.0. (3) STAMP, like most good software, is as notable for what it excludes as for what it includes. We applaud the authors for maintaining STAMP s sharp focus on unobserved components models, and we hope that focus will be maintained in future versions. Nevertheless, the set of models implemented in STAMP could be enlarged without compromising the focus. One is tempted to enlarge the focus to state space models, but that would of course impose almost no discipline, particularly when one allows for nonlinear state space representations, as huge classes of models may be put in state space form. But some models are more naturally and immediately written down in state space form than are others. In fact, that s what STAMP is really about -- models that are naturally written down in state space form from the outset, of which

19 -18- traditional unobserved components models are only one example. Other s include stochastic volatility models (e.g., Taylor, 1986), regime switching models (e.g., Hamilton, 1989), and related multivariate models with latent factor structure (e.g., Diebold and Nerlove, 1989, and Diebold and Rudebusch, 1996). (4) As the list of models implemented in STAMP grows, so too should the list of estimation methods. In particular, the nonlinear models listed in (3) above have challenging likelihood structures, and Markov chain Monte Carlo methods are proving useful for likelihood evaluation (e.g., Kim and Shephard, 1994, and Kim and Nelson, 1995). We look forward to the inclusion of such methods in the next version of STAMP. (5) The perspective of STAMP is entirely classical. STAMP makes extensive use of state-space representations and the Kalman filter to evaluate the likelihood, which is then maximized. It would be nice to allow for the possibility of Bayesian analyses under various priors, which is also facilitated by state-space representations and the Kalman filter, in the spirit of West and Harrison (1989). Markov chain Monte Carlo methods may be very useful in that regard as well.

20 -19- References Diebold, F.X., 1989, Structural Time Series Analysis and Modeling Package: A Review, Journal of Applied Econometrics, 4, Diebold, F.X., 1992, Review of Forecasting, Structural Time Series Models and the Kalman Filter, by A.C. Harvey, Econometric Theory, 8, Diebold, F.X. and M. Nerlove, 1989, "The Dynamics of Exchange Rate Volatility: A Multivariate Latent-Factor ARCH Model," Journal of Applied Econometrics, 4, Diebold, F.X. and G.D. Rudebusch, 1996, Measuring Business Cycles: A Modern Perspective, Review of Economics and Statistics, in press. Doornik, J.A. and D.F. Hendry, 1994a, PcFiml, Version 8.0: Interactive Econometric Modeling of Dynamic Systems (Thomson International Publishing, London). Doornik, J.A. and D.F. Hendry, 1994b, PcGive, Version 8.0: Interactive Econometric Modeling System (Thomson International Publishing, London). Hamilton, J.D., 1989, "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, 57, Harvey, A.C., 1989, Forecasting, Structural Time Series Models and the Kalman Filter (Cambridge University Press, Cambridge). Harvey, A.C. and N. Shephard, 1993, Structural Time Series Models, in G.S. Maddala, et al., eds., Handbook of Statistics, Volume 11 (Elsevier Science Publishers BV, Amsterdam). Kim, C.-J. and C.R. Nelson, 1995, Business Cycle Turning Points, a new Coincident Index, and Tests of Duration Dependence Based on a Dynamic Factor Model with Regime Switching, Manuscript, Department of Economics, University of Washington. Kim, S. and N. Shephard, 1994, "Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models," Manuscript, Nuffield College, Oxford. Koenker, R., 1988, "Asymptotic Theory and Econometric Practice," Journal of

21 -20- Applied Econometrics, 3, Koopman, S.J., A.C. Harvey, J.A. Doornik, and N. Shephard, 1995, Stamp 5.0: Structural Time Series Analyser, Modeller and Predictor (Chapman and Hall, London). Nerlove, M., D.M. Grether, and J.L. Carlvalho, 1979, Analysis of Economic Time Series: A Synthesis (New York, Academic Press). Taylor, S.J., 1986, Modelling Financial Time Series (New York, John Wiley). West, M. and J. Harrison, 1989, Bayesian Forecasting and Dynamic Models (Springer-Verlag, New York).