Question: 7. Consider a standard multiple linear regression model with time series data: yt = Bo B1xt1 ... ktk ut. Assume that Assumptions TS.1, TS.2, TS.3,

7. Consider a standard multiple linear regression model with time series data: yt = Bo B1xt1 ... ktk ut. Assume that Assumptions TS.1, TS.2, TS.3, and TS.4 all hold. i. Suppose we think that the errors {ut} follow an AR(1) model with parameter p and so we apply the Prais-Winsten method. If the errors do not follow an AR(1) model-for example, suppose they follow an AR(2) model, or an MA(1) model why will the usual Prais-Winsten standard errors be incorrect? ii. Can you think of a way to use the Newey-West procedure, in conjunction with Prais-Winsten estimation, to obtain valid standard errors? Be very specific about the steps you would follow. [Hint: It may help to study equation (12.32) and note that, if {ut} does not follow an AR(1) process, et generally should be replaced by ut - put-1, where p is the probability limit of the estimator p. Now, is the error {ut - put-1} serially uncorrelated in general? What can you do if it is not?] iii. Explain why your answer to part (ii) should not change if we drop Assumption TS.4

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