Question

Describe the Cochrane-Orcutt Iterative procedure to correct for first order autocorrelation in the model Yt = B0 + B1X1 + B2X2 + ut

Answer 1

1. Run OLS regression on

Y = B0 +B1X1 + B2X2 + Ut

and find the residuals e₁, e₂

2.  Using these sample residuals ei find an estimate for p using OLS regression on ej= pe(j-1) + uj.

3. Substitute this estimate for ρ in the generalized difference equation

Yi' = B0' + B1Xi1' + B2 Xi2' + ui

4.  Based on 3, new residuals can be calculated then go to 2.

Continue this procedure, which is also called iteration, until the change in the estimated value of ρ is less than some predetermined amount. Note that an iterative approach is used since regression coefficient in 2 is not necessarily an unbiased estimate of ρ, although it is known to be a consistent estimate of ρ i.e. it will coverge to population estimates as the number of observations increase.

also,

Consider the model

Yt = a + BXt + Ut

where Yt is the value of the dependent variable of interest at time t, B is a column vector of coefficients to be estimated, Xt is a row vector of explanatory variables at time t, and Ut is the error term at time t.

If it is found, for instance via the Durbin–Watson statistic, that the error term is correlated, then the inference is invalid because errors are estimated with bias (with the assumption of CLRM the errors should not be correlated with each other. To avoid this problem, the residuals should be fixed in a model. If in the process it is found, Ut = pU(t-1) + et where |p|<1, with the errors being white noise, then the Cochrane–Orcutt procedure can be used to transform the model by taking a quasi-difference:

Yt - pY(t-1) = a(1-p) + B(Xt - pX(t-1) + et