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 Donald Cochrane and Guy Orcutt.
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Theory
Consider the model
where
If it is found via the Durbin–Watson statistic that the error term is serially correlated over time, then standard statistical inference as normally applied to regressions is invalid because standard errors are estimated with bias. To avoid this problem, the residuals must be modeled. If the process generating the residuals is found to be a stationary first-order autoregressive structure,
In this specification the error terms are white noise, so statistical inference is valid. Then the sum of squared residuals (the sum of squared estimates of
Estimating the autoregressive parameter
If
It has to be noted, though, that the iterative Cochrane–Orcutt procedure might converge to a local but not global minimum of the residual sum of squares.