Kindly help me solve this

7. Correcting for serial correlation with strictly exogenous regressors Consider the following standard multiple linear regression model with time series data: y, = e +31%; + +tx\"; +3; Assume that assumptions 15.1,1'52, T53, and EA all hold. Suppose that you believe that the errors {to} follow an AMI} model with parameter p, and so you apply the PraisWinsten method. If the errors do not follow an AR(1) modelforexampie, suppose they follow an AR(2) model, or an MA(1) modelwhich of the following explains why the usual PraisWinsoen standard errors will be incorrect? "_-\" The tlansforrned variables do not have serial correlation. The usual transformation will not fully eliminate the serial correlation in up The regression of the OLS residuals on a single lag consistently estimate the correlation ooeicient. Consider a standard multiple linear regression model with time series data: VI = bo + bixn + ... + box+ Uit. Assume that all the classical assumptions except for no serial correlation hold. (i) Suppose we think that the errors {u} 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-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 note that, if {ut) does not follow an AR(1) process, et generally should be replaced by u - pur-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 homoscedasticity assumption