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Unformatted text preview: STA 4005A Midterm Examination (Total Marks 35) October 25, 2007 Answer ALL questions: Time allowed: 1 1/2 hours. Let a t ∼ NID (0 ,σ 2 a ). 1. Consider a MA(2) model: Z t = a t 1 . 3 a t 1 . 4 a t 2 , σ 2 a = 5 . (a) (2 marks) Find E ( Z t ) and V ar ( Z t ). (b) (3 marks) Find the autocovariance function γ k , k = 1 , 2 , 3 ,... . (c) (2 marks) Find the autocorrelations ρ 1 and ρ 2 . 2. Consider the process Z t = 6+ X t where X t = 1 when t is odd and X t = 0 when t is even. (a) (3 marks) Find the joint distribution function of Z 1 , Z 2 and Z 3 . (b) (2 marks) Is { Z t } strictly stationary? If the answer is YES, prove it. If the answer is NO, explain why. 3. Suppose that a random process { Z t } ( t = 0 , ± 1 , ± 2 , ... ) is defined by Z t αZ t 1 = Y t βY t 2 where α, β are real constants and { Y t } is a process of zero mean uncorrelated random variables with variance σ 2 Y = 4....
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This note was uploaded on 11/02/2011 for the course STAT 4005 taught by Professor Wu,kaho during the Spring '08 term at CUHK.
 Spring '08
 WU,KaHo

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