Question 3 [31 marks] (a) (i) Find the autocorrelation function for the stationary process Y₁ = 10 + e,e-1 + 1e₁-2. (8 m

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Question 3 31 Marks A I Find The Autocorrelation Function For The Stationary Process Y 10 E E 1 1e 2 8 M 1 (36.56 KiB) Viewed 16 times

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Question 3 [31 marks] (a) (i) Find the autocorrelation function for the stationary process Y₁ = 10 + e,e-1 + 1e₁-2. (8 marks) (1 marks) (ii) Identify the model in a(i). (b) Consider the AR (2) process y, = 1 + 1.3y-1-0.4y-2+u,, te Z, with u,~ N(0, 1). (i) Determine E (y,). (4 marks) (ii) Determine Var (y₁). (2 marks) (2 marks) (iii) Is y, stationary? Explain your answer. (iv) Determine p₁ and P2. (6 marks) (c) For each of the ARIMA models below, give the values for E(VY,) and Var(VY₁). (i) Y₁ = 3+Y₁-1+e; -0.7e-1 (2 + 2 marks) (ii) Y, = 10 +1.25Y₁-1-0.25Y-2 + e, -0.1e-1 (2 + 2 marks)