Question 3 [33 Marks] (a) Let (e) be a zero-mean, unit-variance white noise process. Consider a process that begins at t

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Question 3 33 Marks A Let E Be A Zero Mean Unit Variance White Noise Process Consider A Process That Begins At T 1 (225.97 KiB) Viewed 28 times

Question 3 [33 Marks] (a) Let (e) be a zero-mean, unit-variance white noise process. Consider a process that begins at time t = 0 and is defined recursively as follows. Let Yo = cieo and Y₁ = c₂Yo + e₁. Then let Y = 91Y-1 +92Y-2 + e, for t > 1 as in an AR (2) process. Show that the process mean is (5 marks) zero. (b) Suppose that (Y,) is generated according to Y, = 10 + e, - e,-1+e-2, with e, ~ N(0, 1). (i) Identify the model Y₁. (ii) Find the mean and covariance functions for (Y). Is (Y) stationary? (iii) Find the mean and covariance functions for (VY,). Is (VY,) stationary? (vi) Determine P1 and P2. (v) Using (vi) or otherwise, determine 11 and 22. (2 marks) (2+5+1 marks) (2+5+1 marks) (6 marks) (4 marks)