Consider the population regression model: Yi = 0 + 1Xt + t Where the error term may be written as t= t-1 + ut with E(t) = E(ut) = 0, Cov (Xt, t) = Cov (Ut, t) = 0, Var(t) = 2 , and Var (ut) = 2 u for all t.

a. Prove that this model suffers from autocorrelation

b. What is autocorrelation and what will be the consequence(s) of estimating the above model with OLS?

c. Describe how you would test for the presence of autocorrelation, and explicitly state whatever assumptions you are making to ensure the validity of the test.

d. How do you perform the Durbin-Watson test for autocorrelation? Explain.