Economics 2122A/B Lecture : 398_39_solutions-instructor-manual_13-introduction-nonstationary-time-series_im_ch13.pdf
16 Jan 2014
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Answer: the expected value of xt is 0 and therefore independent of time: Since t and t 1 are uncorrelated, and this is independent of time. Xt 1 = t 1 + 2 t 2, the population covariance of xt and xt 1 is given by. The population covariance between xt and xt s is 0 for all s > 1 because xt and xt s have no elements in common if s > 1. Thus the third condition for stationarity is also satisfied. All ma processes are stationary, the general proof being a simple extension of that for the ma(1) case. , has initial value x0, where x0 is defined as. Demonstrate that x0 is a random draw from the ensemble distribution for x. Answer: lagging and substituting, it was shown, equation (13. 12), that. With the stochastic definition of x0, we now have. Given the generating process for x0, one has and.
