midterm_soln

# midterm_soln - PSTAT 174 / 274 - Midterm Solution 1. yt =...

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PSTAT 174 / 274 - Midterm Solution 1. y t = x t = x t - x t - 1 = β 2 + w t - w t - 1 E ( y t ) = β 2 Cov ( y t ) = 2 σ 2 , h = 0 - σ 2 , h = ± 1 0 , otherwise 2. ρ ( h ) = 0 . 4 h ,h = 0 , ± 1 , ··· φ hh = ( 0 . 4 , h = 1 0 , otherwise 2 4 6 8 10 0.0 0.2 0.4 0.6 0.8 1.0 ACF Lag ACF (a) 2 4 6 8 10 0.1 0.3 PACF Lag PACF (b) 3. AR(2) model - ACF tails oﬀ and PACF cuts oﬀ after h = 2. You can also claim ARMA(1,1) if you see ACF and PACF tails oﬀ. 1

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4. x n n +1 = 0 . 2 x n + 0 . 3 x n - 1 MSE = E (( x n +1 - 0 . 2 x n - 0 . 3 x n - 1 ) 2 ) = γ (0) - γ 0 n Γ - 1 n γ n = 1023 . 75 , γ n = ˆ γ (1) γ (2) ! , Γ = ˆ γ (0) γ (1) γ (1) γ (0) ! γ (0) = 1225 ρ (1) = 0 . 2 ρ (0) + 0 . 3 ρ (1) = 2 / 7 γ (1) = ρ (1) × γ (0) = 350 ρ (2) = 0 . 2 ρ (1) + 0 . 3 ρ (0) = 0 . 3571429 γ (2) = ρ (2)
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## This note was uploaded on 05/01/2009 for the course PSTAT 120A taught by Professor Mackgalloway during the Spring '08 term at UCSB.

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midterm_soln - PSTAT 174 / 274 - Midterm Solution 1. yt =...

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