ECON 483: Forecasting

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Homework assignment 4

The data for the homework assignment is available in EasyReg space delimited text format (*) and in Excel CSV format (**). You may treat the time series involved as an annual time series, starting from year 1. This time series is generated as a stationary AR(p) process, with p £ 10:

where the errors U_t are independent standard normally distributed.

1. Determine p on the basis of the partial autocorrelation function.
2. Check your choice of p on the basis of information criteria, using the EasyReg option "ARIMA model selection via information criteria".
3. Given your choice of p, estimate the model by OLS (using the "Linear Regression" option of your econometrics software), and test whether some lagged dependent variables can be deleted from the model.
4. If so, re-estimate the model by OLS without the insignificant lagged dependent variables, and guess how the time series was generated.
5. Re-estimate this "cleaned-up", model via the EasyReg ARIMA module, using the first 490 observations.
   (Note that if you include a constant term in the model, the parameter b(1) in the EasyReg output is the estimate of E[Y_t] = b₀ / (1 - b₁ - b₂ - .... - b_p) rather than the intercept b₀ in the OLS regression.)
6. Forecast the last 10 observations, in two ways, via
   • the one-step ahead forecast option, and
   • the recursive forecast option,
   in the "What to do next?" window.
7. Discuss the quality (or lack thereof) of the forecasts.

(*) Click on the link, and save the file as a text file on your hard disk via the "Save as .." option of your web browser. Note that Internet Explorer will try to save the file as a web page (*.htm format). You have to overrule that.

(**) If you use Internet Explorer and you click on the link the file will be automatically imported in Excel, provided that you have installed Excel. Then use the "Save as .." option of Excel to save the file on your hard disk. Netscape and Mozilla Firefox will display the file as a text file. Therefore, if you use Netscape or Firefox follow the procedure under (*).