Consider a standard multiple linear regression model with time series data:

Assume that Assumptions TS.1, TS.2, TS.3, and TS.4 all hold.
(i) Suppose we think that the errors {u_t) follow an AR(1) model with parameter ρ 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.
(iii) Explain why your answer to part (ii) should not change if we drop Assumption TS.4.

y, = Bo + BX + + B + u,. ...