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Unformatted text preview: tionary, giving full justiﬁcation X t = 13 4 X t13 4 X t2 + ± t . 1 5. HARDER QUESTION Let { X t } be the zero mean autoregressive process of order 2 deﬁned by X t( g 1 + g 2 ) X t1 + g 1 g 2 X t2 = ± t , where  g 1  ,  g 2  < 1 , and { ± t } is white noise with mean zero and variance σ 2 ± . (a) Explain why { X t } is stationary. (b) Show that { X t } can be written in the general linear model form X t = ± 1 g 2g 1 ! ∞ X k =0 ² g k +1 2g k +1 1 ³ ± tk . (c) Hence show that the autocovariance sequence takes the form s τ = ± σ 2 ± g 2g 1 ! g  τ  +1 2 (1g 2 1 )g  τ  +1 1 (1g 2 2 ) (1g 2 1 )(1g 2 2 )(1g 1 g 2 ) τ = 0 , ± 1 , ± 2 , ... 2...
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 Spring '09
 jsdkasj
 Covariance, Variance, Autocorrelation, 1 K, Stationary process, τ, Xt

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