solutions3 - Matlab Solutions Time Series (2DD23) Exercise...

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Matlab Solutions Time Series (2DD23) Week 3 Exercise 3.1 The formula of the autocorrelationfunction is: ρ( k ) = γ( k ) γ( 0 ) . γ( k ) = Cov ( X t , X t + k ) = Cov ( Z t + 0 . 7 Z t - 1 - 0 . 2 Z t - 2 , Z t + k + 0 . 7 Z t + k - 1 - 0 . 2 Z t + k - 2 ) Now use the formula: Cov ( X 1 + X 2 , Y ) = Cov ( X 1 , Y ) + Cov ( X 2 , Y ) . γ( k ) = Cov ( Z t , Z t + k ) + Cov ( Z t , 0 . 7 Z t + k - 1 ) + Cov ( Z t , - 0 . 2 Z t + k - 2 )) + Cov ( 0 . 7 Z t - 1 , Z t + k ) + Cov ( 0 . 7 Z t - 1 , 0 . 7 Z t + k - 1 ) + Cov ( 0 . 7 Z t - 1 , - 0 . 2 Z t + k - 2 )) + Cov ( - 0 . 2 Z t - 2 , Z t + k ) + Cov ( - 0 . 2 Z t - 2 , 0 . 7 Z t + k - 1 ) + Cov ( - 0 . 2 Z t - 2 , - 0 . 2 Z t + k - 2 )) Now use Cov ( aX , Y ) = a Cov ( X , Y ), Cov ( X , X ) = Var ( X ) and for k 6= 0 : Cov ( Z t , Z t + k ) = 0 . The case k = 0 : γ( k ) = Cov ( Z t , Z t ) + 0 . 7 Cov ( Z t , Z t - 1 ) - 0 . 2 Cov ( Z t , Z t - 2 )) + 0 . 7 Cov ( Z t - 1 , Z t ) + 0 . 7 2 Cov ( Z t - 1 , Z t - 1 ) - 0 . 14 Cov ( Z t - 1 , Z t + k - 2 )) - 0 . 2 Cov ( Z t - 2 , Z t ) - 0 . 14 Cov ( Z t - 2 , Z t + k - 1 ) + ( -
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solutions3 - Matlab Solutions Time Series (2DD23) Exercise...

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