Cochrane-Orcutt estimation

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.

Theory
Consider the model


 * $$y_{t}=\beta+X_{t}\gamma+\varepsilon_{t},\,$$

where $$y_{t}$$ is the time series of interest at time t, $$\gamma$$ is a vector of coefficients, $$X_{t}$$ is a matrix of explanatory variables, and $$\varepsilon_{t}$$ is the error term. The error term can be serially correlated over time: $$\varepsilon_{t}=\rho \varepsilon_{t-1}+e_{t},\ |\rho|<1$$. The Cochrane-Orcutt procedure transforms the model:


 * $$y_{t}-\rho y_{t-1}=\beta(1-\rho)+\gamma(X_{t}-\rho X_{t-1})+e_{t}.$$

Then the sum of squared residuals $$e_{t}^{2}$$ is minimized with respect to $$(\beta,\gamma)$$, conditional on $$\rho$$.

Literature

 * Cochrane and Orcutt. 1949. Application of least squares regression to relationships containing autocorrelated error terms. Journal of the American Statistical Association 44, pp 32-61