Cochrane–Orcutt estimation is a procedure in econometrics, which adjusts a linear model for serial correlation in the error term. It is named after statisticians D. Cochrane and G. H. Orcutt, who worked in the Department of Applied Economics, Cambridge (U.K.).
Contents |
Consider the model
where is the time series of interest at time t, is a vector of coefficients, is a matrix of explanatory variables, and is the error term. The error term can be serially correlated over time: . The Cochrane–Orcutt procedure transforms the model:
Then the sum of squared residuals is minimized with respect to , conditional on .
If is not known, then it is estimated by first getting the residuals of the model and regressing on , leading to an estimate of and making the transformed regression sketched above feasible. This procedure can be done until in consecutive steps of estimating the correlation coefficient no substantial change is observed. Note that this procedure is designed for an AR(1) error term structure and you would lose the first observation, which might be important for small samples.