Upper left area. It is R Script. Here you will write the code. 1. The goal of this problem set is to learn how to use HP filter in R.

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1 Instructions Setting up R Follow these steps if you are new with R: 1. Install R using the following link Make sure to select the version compatible with your operative system. For Windows users: click Download R for Windows - Base and download R version. Install R. For Mac users: click Download R for (Mac) OS X and download R pkg or newer version. Install R. 2. Install R Studio. Use the following link: download/. Make sure you install the version compatible with your OS. 3. Open R Studio. You will see four main areas. Upper left area. It is R Script. Here you will write the code. Lower left area. It is R console. Here you will see how the code runs line by line and if any errors occur. You will also see the output of your code here. Upper right area. Environment contains all the objects you are currently working with (data sets, matrices, formulas, etc.). You can also see R history. Lower right area. All additional tools are here. You can use "Help" tab, type the name of a command or formula if you need information. Plots generated by the code will also appear in this area. Returning to the problem set 1. The goal of this problem set is to learn how to use HP filter in R. 2. Download all the files and save them in a new folder created on your computer. 3. Open file data.csv. It is your data set, but it is partly empty. First, you need to fill the gaps. 1

2 You already have real GDP and Unemployment rate for USA. Collect time series for Consumer Price Index (CPI) for USA. You can use FRED website. Insert this data into column 4 of you table. Collect time series for real GDP, Unemployment rate and Consumer Price Index for a country of a choice. Fill columns 5-7. Make sure that you insert the data only. DO NOT delete any columns, DO NOT change the names of the columns. You can adjust the time interval, if needed. Save the file. Make sure you save the file as data.csv in CSV(Comma delimited) format. Your data set is ready. 4. Open R Studio. Open R script hpfilter.r. To do this, click File - Open and browse the file. 5. Now you should be ready to run the code. Look at the following part of the R Script. ### This is the code for HP filter exercise # Enter the name of the country of your choice : country <-" Belarus " Change the name of the country to the name of the country of your choice (not USA!). 6. Next, the code changes the working directory, using command setwd. Change the working directory to the folder you have created in Step 1. # Change working directory to your folder : setwd ("C:/ Users / mariy / Desktop / hpfilter ") # read the data file data <- read. csv (" data. csv ") Note that R uses slash "/" instead of regular slash "\". 7. Now the code takes the numerical part of the data, omitting the time variable, and takes natural log of all variables. You do not need to make any changes in this part of the code. 2

3 # ######### Install nesessary packages install. packages (" mfilter ") library ( mfilter ) # take natural log of all variables : data <- data [,c(2:7)] cols <- names ( data ) data [ cols ] <- log ( data [ cols ]) 8. The code pick ups the name of the country you have inserted earlier and changes the names of the columns accordingly. Note that three first columns are for USA and does not depend on the country of your choice. You do not need to make any changes in this part of the code. # change the names of the columns : newnames <-c(" loggpd _ USA ", " logunempl _ USA ", " logcpi _ USA ", paste (" loggdp _", country, sep ="", collapse = NULL ), paste (" logunempl _", country, sep ="", collapse = NULL ), paste (" logcpi _", country, sep ="", collapse = NULL )) colnames ( data )<- newnames 9. You have finished the data preparation part of the code. To make sure that everything works fine, you can run this part of the code. To do this, highlight the desired part of the R Script and click "Run" (or Ctrl+Enter). 10. You are ready to apply HP filter. R uses the function hpfilter(x, freq=lambda). Argument x is the time series, the second argument is the parameter λ. # apply HP Filter to real GDP in USA : ### real GDP in USA is stored in data, column 1. # Apply hpfilter to this column : 3

4 HP <- hpfilter ( data [,1], freq =1600) ### here I simply change the name of the series to a nicer one for # the future plot. USA GDP is in column one, so use one here : HP$xname <- newnames [1] All our data are stored in the object data, and the time series loggdp_us is the first column in this large "matrix". This is why the first argument in hpfilter is data[,1]. It means we take all observations from column 1 in our data set. The second argument means that we take λ = If you are using quarterly data, set λ = 1600, if the data is monthly, set λ = 14400, if the data is annual, set λ = The plot should appear in the lower left area of R studio: ### now we are ready to plot the result : plot (HP, ask =F) 12. Now you can save the plot. To do this, run: ### to save the result, run the following code : jpeg ( file =" usa _ gdp _ HPfilter. jpeg ", quality =100, height =650, width =700 ) plot (HP, ask =F) dev. off () The file usa_gdp_hpfilter.jpeg should appear in your folder. You do not need to make any changes in this part of the code. 13. Now save the filtered data. To do this, run: ### you can save your filtered data : HP <- cbind (HP$x, HP$trend, HP$ cycle ) colnames (HP)<-c( newnames [1], " trend ", " cycle ") write. csv (HP, file =" GDP _ USA _ filtered. csv ") The file GDP_USA_filtered.jpeg should appear in your folder. 14. Now you can apply HP filter to the next time series. Log unemployment rate in USA in stored in column 2 in our data set. Run the following code: 4

5 HP <- hpfilter ( data [,2], freq =1600) HP$xname <- newnames [2] ### now we are ready to plot the result : plot (HP, ask =F) ### to save the result, run the following code : jpeg ( file =" usa _ unempl _ HPfilter. jpeg ", quality =100, height =650, width =700 ) plot (HP, ask =F) dev. off () # save HP <- cbind (HP$x, HP$trend, HP$ cycle ) colnames (HP)<-c( newnames [2], " trend ", " cycle ") write. csv (HP, file =" UNEMPL _ USA _ filtered. csv ") Note the the only difference from the code above is that now we refer to the column 2 in our data set, because the unemployment rate for USA is stored there. Also we changed the names of the output files. 15. The code applied HP filter for 2 variables: GDP and the unemployment rate in USA. You need to apply HP filter to four remaining variables in your data set. To do this, you need to change the reference to the column of your data set and the names of the files where you want to store your output. That is it! What to hand in Create a pdf file that contains 6 plots for each time series. For example, the plot for real US GDP looks like this: 5

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