**Cochrane-Orcutt Estimation**

**Definition of Cochrane-Orcutt Estimation:** Cochrane-Orcutt estimation is an algorithm for estimating a time series linear regression in the presence of auto-correlated errors. The implicit citation is to Cochrane-Orcutt (1949).

Suppose we wish to regress y[t] on X[t] in the presence of auto-correlated errors. Run an OLS regression of y on X and construct a series of residuals e[t]. Regress e[t] on e[t-1] to estimate the auto-correlation coefficient, denoted p here. Then construct series y^{*} and X^{*} by: y^{*}_{1} = sqrt(1-p^{2})y_{1},

X^{*}_{1} = sqrt(1-p^{2})X_{1},

and

y^{*}_{t} = y_{t} - py_{t-1},

X^{*}_{t} = X_{t} - pX_{t-1}

One estimates b in y=bX+u by applying this procedure iteratively -- renaming y^{*} to y and X^{*} to X at each step, until estimates of p have converged satisfactorily.

Using the final estimate of p, one can construct an estimate of the covariance matrix of the errors, and apply GLS to get an efficient estimate of b.

Transformed residuals, the covariance matrix of the estimate of b, R^{2}, and so forth can be calculated.

**Terms related to Cochrane-Orcutt Estimation:**