Cochrane-Orcutt Estimation <Back to Last Page>     <Full Glossary>

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

The procedure is nicely explained in the SHAZAM manual section online at the SHAZAM web site. Their procedure includes an improvement to include the first observation attributed to the Prais-Winsten transformation. A summary of their excellent description is below. This version of the algorithm can handle only first-order autocorrelation but the Cochrane-Orcutt method could handle more.

Suppose we wish to regress y[t] on X[t] in the presence of autocorrelated 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 autocorrelation coefficient, denoted p here. Then construct series y^* and X^* by: y^*₁ = sqrt(1-p²)y₁,
X^*₁ = sqrt(1-p²)X₁,

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, R², and so forth can be calculated.

(Econterms)

Terms related to Cochrane-Orcutt Estimation:

• Prais-Winsten transformation
• OLS
• GLS

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