ing with autocorrelation VI Exercise 12 What should be S in the particular case of the Cochrane-Orcutt method? Follow the steps to answer that question: 1. Write the AR(1) model of equation 15 as a function of lag values of Ut. 2. Use the properties of ut to get V(ut). 3. Compute Cov(ut, Ut-1). 4. Deduce Cov( Ut, Ut-j). 5. Finally, deduce n. it = put-, + Vt = P[Put2 + VE-2] tre k - 1 = P uf* +P ut-kt/ T .... TV'sDealing with autocorrelation IV 3. The return of the Generalized Least Squares (GLS) . We consider the regression model Y = XB+u ( 17 ) where the variance is V(u) = Ru. . The vector of the estimated parameters is BGLS = (X'n,1X)-1X'n,ly . The estimator of the variance-covariance matrix of the parameter is V ( B ) = (X's2,]x) -1 . The GLS estimator is BLUE and if u = 021, we get back the OLS estimator.revealing with autocorrelation V . The GLS are a generalized version of the OLS. . The criterium to minimize is: Min(y - XB)'Sul(y - XB) . We associate the larger weights to the lower variances of y. If Su = 021, we minimize the ESS, and we get back to the OLS minimization problem. 102 Ou1 , U2 0 UI , UT 0 u1 , U2 0 U2 , UT If fu = 0 U1 , UT 0 U2 , UT Once again, S is unknown and we can only apply the GLS only if we have a convergent estimator of $2. The Cochrane-Orcutt procedure is a way to get a consistent estimator of 1