• Problem 3.9 • For the AR(2) model given by by Xt = −.9Xt−2 + Zt , find the roots of the characteristic polynomial, and then plot its ACF • Suppose that the daily log return of a security follows the model rt = 0.01 + 0.2rt−2 + Zt where Zt is a Gaussian white noise series with mean zero and variance 0.02. What are the mean and variance of the return series rt ? Compute the lag-1 and lag-2 autocorrelations of rt . • Consider the monthly US unemployment rate from Jan 1948 to March 2009. The data are seasonally adjusted and obtained from the Federal Reserve Bank of St. Louis. Build a time series model for the series. Does the final model imply the existence of business cycles?Why? 1
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