Midterm 2 Answers

Midterm 2 Answers - plus and minus 2 p 2 2 x + 2 . 3. (a) H...

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Economics 467: Economic Forecasting State University of New York at Binghamton Department of Economics Spring 2010 Midterm II — Answers 1. (a) ln L ( Θ )= T 2 ln 2 π T 2 ln σ 2 1 2 σ 2 T X t =1 ( y t c φy t 1 θε t 1 ) 2 (b) In OLS we want to minimize SSR = T X t =1 ε 2 t .H e r eln L ( Θ ) is a function of SSR and hence we want to maximize T X t =1 ( y t c φy t 1 θε t 1 ) 2 . (c) ln L ( Θ )= T 2 ln 2 π T 2 ln σ 2 1 2 σ 2 T X t =1 ( y t c φy t 1 ) 2 (d) LR = 2 [ln L R ( Θ ) ln L U ( Θ )] χ 2 1 (e) Yes. LR > 0b e cau s eln L U ( Θ ) > ln L R ( Θ ). More information cannot be worse than less information. 2. y t + h = μ + βx t + h + ε t + h (a) b y t + h | t = E ( y t + h | t )= E ( μ + βx t + h + ε t + h | t )= μ h (b) e t + h = y t + h b y t + h | t = μ + βx t + h + ε t + h μ = βx t + h + ε t + h h (c) V ( e t + h )= V ( βx t + h + ε t + h )= β 2 σ 2 x + σ 2 ε h (d) P h b y t + h | t 2 p β 2 σ 2 x + σ 2 ε <y t + h < b y t + h | t +2 p β 2 σ 2 x + σ 2 ε i = P h μ 2 p β 2 σ 2 x + σ 2 ε <y t + h +2 p β 2 σ 2 x + σ 2 ε i 0 . 95 h (e) A plot of
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Unformatted text preview: plus and minus 2 p 2 2 x + 2 . 3. (a) H : 3 = 4 = 5 = 6 = 0 (b) LM = l F = l ( R 2 U R 2 R ) / ( l ) ( 1 R 2 U ) / ( T k 1) = l ( SSR R SSR U ) /l SSR U / ( T k 1) 2 l LM = 4 (0 . 929 . 923) / 4 (1 . 929) / (181 8 1) = 4 (154 . 4 141 . 1) / 4 154 . 4 / (181 8 1) 14 . 81 (c) There is no autocorrelation in the residuals. Correctly speci f ed. (d) There is autocorrelation in the residuals. Incorrect speci f cation. (e) If we fail to reject then we move onto forecasting. If we reject the null we must f nd a new tenative model. 1...
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