TS Module 11 Simulated and actual time series
(The attached PDF file has better formatting.)
Specification of simulated time series
Specification of actual time series
Read Section 6.3, “Specification of simulated time series,” on pages 117-124. The text shows how to use correlograms to identify the time series. You use these tools for your student project.
Read Section 6.4, “Non-stationarity,” on pages 124-128.
Know the problems of over-differencing on pages 126-128. Some student projects make this error at first. A candidate may feel that the correlogram does not approach zero fast enough and takes a second difference. Sometimes this is correct; more often it is wrong.
Be sure that differencing is warranted in your project. If you take a second difference, say why it is justified. The time series may be a combination of two ARIMA(1,1,0) processes with different values for ì or ö. Takings second differences obscures the true parameters.
For your student project, consider taking logarithms before first differences. If you have a long enough time series, such as average claim severities in nominal dollars for forty years, you see the exponential curve. For a short time series, such as twelve months of daily stock prices, you won’t see the exponential pattern in the sample points.
The final exam does not test the Dickey-Fuller Unit-Root test on pages 128-130. You may want to use this tool in your student project, though. It provides a quantitative test for non-stationarity that you may use in addition to graphic analsis.
Read Section 6.6, “Specification of actual time series,” on pages 133-140. The final exam does not test these time series, but this section helps you in your student project.