ECON 483: Forecasting

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Empirical homework assignment 10

The data for the homework assignment is available in EasyReg (former) default format (*) and in Excel CSV format (**). This data file contains the monthly time series "Exchange rate UK/US" (= British pounds per $100), from month 1973.01 to month 1995.09.

You may assume that there are no seasonal effects in this time series.

Assignments:

1. To be able to forecast the exchange rate in months 1995.10, 1995.11 and 1995.12, add three missing value to the data, via Menu > Input > Prepare time series for forecasting.
2. Because the exchange rate is always positive, transform it by taking the log transformation, and verify that the log of the exchange rate UK/US is a unit root process, using the ADF test as well as the Breitung test.
   • Why do you need to make the time series unbounded?
   • Against which alternative (zero mean stationarity, stationarity about a constant, or trend stationarity) would you test the unit root hypothesis ?
3. Take the first difference of the log of the exchange rate, and estimate an AR(p) model for the transformed time series.
   • Determine p.
   • Would you include an intercept? Motivate your answer.
4. Re-estimate the model with (G)ARCH errors, and choose the most parsimonious specification¹ for the conditional variance involved. When done, write the estimated AR-(G)ARCH errors U_t to the data file.
5. Forecast the first difference of the log of the exchange rate for month 1995.10.
6. Take the square of the estimated AR-(G)ARCH errors U_t and re-estimate the (G)ARCH model for these squared errors.
7. Forecast the conditional variance s_t² of U_t for months 1995.10, 1995.11 and 1995.12.

(1) This means the specification with the minimum number of parameters.

(*) 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 (*).