(a) Let {e} be a zero-mean, unit-variance white noise process. Consider a process that begins at time t = 0 and is defin

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A Let E Be A Zero Mean Unit Variance White Noise Process Consider A Process That Begins At Time T 0 And Is Defin 1 (47.37 KiB) Viewed 20 times

(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 = c₁eo and Y₁ = c₂Yo + €₁. Then let Y₁ = 9₁Y₁-1 + Q₂Y₁−2+ 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 Y₁ = 10 + e, − zer−1 + fer-2, with e, ~ N(0, 1). t-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 {VY₁}. 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)