Definition of CochraneOrcutt Estimation: CochraneOrcutt estimation is an algorithm for estimating a time series linear regression in the presence of autocorrelated errors. The implicit citation is to CochraneOrcutt (1949).
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[t1] to estimate the autocorrelation coefficient, denoted p here. Then construct series y^{*} and X^{*} by: y^{*}_{1} = sqrt(1p^{2})y_{1},
X^{*}_{1} = sqrt(1p^{2})X_{1},
and
y^{*}_{t} = y_{t}  py_{t1},
X^{*}_{t} = X_{t}  pX_{t1}
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 CochraneOrcutt Estimation:
 PraisWinsten transformation
 GLS

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