For each of the four AR(2) time series of length N = 1024 shown in Figure 34, compute the periodogram over the grid of frequencies f˜ k = k/(2N), k = 0, 1, . . . , 2N − 1 (the series are downloadable...

For each of the four AR(2) time series of length N = 1024 shown in Figure 34, compute the periodogram over the grid of frequencies f˜ k = k/(2N), k = 0, 1, . . . , 2N − 1 (the series are downloadable from the “Data” part of the website for the book). Based upon each of the four periodograms, use the circulant embedding method to generate a simulated series whose theoretical SDF is equal to the periodogram (this method gives two simulated series, but just pick one of them for subsequent use). Compute the period grams for each of the four simulated series. Compare these periodograms to the corresponding period grams for the four actual AR(2) time series. Repeat this exercise using the four AR(4) series in Comment upon your finding.