Spring Solution Homework.pdf

# Hence the acf of x t is given by ρ x k γ x k γ x 0

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Hence, the ACF of X t is given by ρ X ( k ) = γ X ( k ) γ X (0) = ( Φ h , k = 4 h 0 , otherwise. To find γ X (0) , we calculate E [ Z t X t ] = E h j =0 Φ j Z t - 4 j Z t i = j =0 Φ j E [ Z t - 4 j Z t ] = Φ 0 σ 2 Z = σ 2 Z . We now have: γ X (0) = Φ γ X (4) + σ 2 Z Φ 2 γ X (0) + σ 2 Z or γ X (0) = σ 2 Z 1 - Φ 2 , γ X (4 h ) = Φ h σ 2 Z 1 - Φ 2 . This study resource was shared via CourseHero.com Powered by TCPDF ( )
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• Spring '17
• Sams
• ........., sh, ed d, ACF

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