A5 soln - STA4005B Assignment 5 (Solution) 1a) Method of...

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STA4005B Assignment 5 (Solution) 1a) Method of moment: t t a Z B B + = β φ ) 1 )( 1 ( Let , then t t Z B W ) 1 ( = t t a W B + = ) 1 (. 926742 . 8 = W , 23263 . 13 2 = S Autocorrelation matrix: Lag W t 0 1 1 0.642786 2 0.321236 3 0.245584 4 0.237506 5 0.255553 Since is a AR(1) process, we let t W t t t a W W + = ) ( ) ( 1 µ 188757 . 3 ) 642786 . 0 1 ( 926742 . 8 ) ˆ 1 ( ˆ ˆ 765252 . 7 ) 23263 . 13 )( 642786 . 0 1 ( ) 1 ( ˆ 642786 . 0 ˆ 926742 . 8 ˆ 1 2 2 2 1 2 1 = = = = = = = = = = σ S r r W a 1b) Conditional least squares: t t a W B + = ) 1 t t t t t t a W W a W W + + = + + = 1 1 0 1 where = = 1 0 ,. *** Linear Model *** Call: lm(formula = Wt ~ Wt.1, data = SDF1, na.action = na.exclude) Residuals: Min 1Q Median 3Q Max -7.177 -1.666 -0.1061 2.309 5.807 Coefficients: Value Std. Error t value Pr(>|t|) (Intercept) 3.2367 0.7801 4.1490 0.0001 Wt.1 0.6454 0.0811 7.9546 0.0000 Residual standard error: 2.763 on 86 degrees of freedom Multiple R-Squared: 0.4239 F-statistic: 63.27 on 1 and 86 degrees of freedom, the p-value is 6.536e-012 Thus 6454 . 0 ˆ ˆ 1 = = , , 2367 . 3 ˆ ˆ 0 = = 6342 . 7 763 . 2 ) ( 2 2 2 = = = MSE a
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2) Let the AR(2) model be t t t t a Z Z Z + + + = ) ( ) ( 2 2 1 1 µ φ The above equation can be rewritten as: t t t t a Z Z Z + + = ) ( ) ( ) ( 2 2 1 1 Consider the Yule Walker equation and replace
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A5 soln - STA4005B Assignment 5 (Solution) 1a) Method of...

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