For a fixed, positive integer r and constant φ, consider the time series defined by Yt et φet 1– φ2et 2–… φret r– = + + + + . (a) Show that this process is stationary for any value of φ. (b) Find the autocorrelation function.
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Suppose e_t is white noise with E(e_t)=0, Var(e_t)=σ^2, and Y_t = sum_{k=0}^r φ^k e_{t-k} = e_t + φ e_{t-1} + φ^2 e_{t-2} + ... + φ^r e_{t-r}. This is an MA(r) process with coefficients θ_k = φ^k for k = 0,1,...,r. Show more…
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