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Unformatted text preview: Homework 8 8.11 a. σ 2 t = α 1 + α 2 S t + α 3 D t + α 4 S 2 t + α 5 ( S t × D t ). Note that D 2 t is not used here because it is a dummy variable. b. α 2 = α 3 = α 4 = α 5 = 0. c. Regress P t against a constant, S t , and D t and obtain ˆ u t = P t ˆ β 1 ˆ β 2 S t ˆ β 3 D t . Next regress ˆ u 2 t against a constant, S t , D t , S 2 t and ( S t × D t ). d. Compute LM = nR 2 , where n is the number of observations and R 2 is the unadjusted R 2 from the second regression in Step c. Under the null hypothesis of homoscedas ticity, LM has the χ 2 distribution with 4 d.f. e. The critical value of χ 2 4 for a 5% level is 9.48773. Reject the null if LM > 9 . 48773. f. From the auxiliary regression compute σ 2 t = ˆ α 1 + ˆ α 2 S t + ˆ α 3 D t + ˆ α 4 S 2 t + ˆ α 5 ( S t × D t ). Next compute the weight as w t = 1 / q ˆ σ 2 t . Finally, regress w t P t against w t , w t S t and w t D t , without a constant term. 8.12 a. H : α 2 = α 3 = 0. H 1 : At least one of them is not zero. b. (1) Regress E t against a constant and Y t , (2) compute the residuals ˆ u t = E t ˆ β 1 ˆ β 2 Y t , and (3) regress ˆ u 2 t against a constant, P t and P 2 t ....
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 Summer '07
 Rashidian
 Econometrics, Regression Analysis, Trigraph, Autocorrelation, LM, regress wt

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