Question: TIME SERIES (d) Consider the AR(1) process Zt = oZt-1 + at. (i) Show that the ACF of process satisfies the difference equation Pk -

TIME SERIES

(d) Consider the AR(1) process Zt = oZt-1 + at. (i) Show that the ACF of process satisfies the difference equation Pk - OPK_1 = 0 for k 2 1. (ii) Find the general expression for Pk. (iii) Find the ACF p, and plot it for k = 0, 1, 2, 3, 4, 5, for Zt = -0.5Zt-1 + at , where at is a Gaussian noise process. QUESTION 2 Sketch the autocorrelation functions for the following MA(2) models with parameters as specified below. What is your observation? (i) 01 = 0.5 and 02 = 0.4. (ii) 01 = 1.2 and 02 = 0.7. (iii) 01 = -1 and 02 = -0.6

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