Exercise 5 of Assignment 5 (due 2/11/08)

Compute an sdf estimate of the AR(4) time series $X_t$ using the idea of prewhitening (Section 6.5) via the following steps (note that this series can be downloaded via the `Data and Data Tapers' section of the Web page for the course).

1. Filter $X_t$ using the prewhitening filter $g_0 = 1.0$ and $g_1 = -0.9$ to obtain the prewhitened series $Y_t$.
2. Compute the periodogram for $Y_t$ and then postcolor it to create an estimate for the sdf of $X_t$. Plot this estimate in a manner similar to the two plots in Figure 227.
3. Comment on how well this estimate of the sdf for $X_t$ compares to the two estimates plotted in Figure 227.

Finally, repeat all of the above using the prewhitening filter $g_0 = 1$ and $g_1 = -1$. Does it matter which of these two prewhitening filters we use here?

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