Cochrane–Orcutt estimation

Cochrane–Orcutt estimation is a statistical procedure used to correct for autocorrelation in the residuals of a linear regression model. Autocorrelation, also known as serial correlation, occurs when the residuals (errors) of a regression model are not independent of each other. This violation of the classical linear regression assumptions can lead to biased and inefficient estimates of the regression coefficients. The Cochrane–Orcutt procedure, named after Donald Cochrane and Guy H. Orcutt who introduced the method in 1949, is one of the techniques used to address this issue.

Overview

The Cochrane–Orcutt estimation is an iterative method that aims to transform the original regression model in such a way that the transformed model's residuals are no longer autocorrelated. The procedure starts with an initial estimation of the regression model, followed by an estimation of the autocorrelation coefficient. This coefficient is then used to transform both the dependent and independent variables of the model. A new regression is run on these transformed variables, and the process is repeated until the estimates of the coefficients converge to stable values.

Procedure

1. Estimate the original linear regression model and compute the residuals.
2. Estimate the autocorrelation coefficient (\(\rho\)) of the residuals.
3. Transform the original variables using the estimated autocorrelation coefficient.
4. Re-estimate the regression model using the transformed variables.
5. Repeat steps 2-4 until the estimates converge.

Application

The Cochrane–Orcutt procedure is widely used in econometrics and other fields where time series data are analyzed. It is particularly useful when dealing with economic and financial data, which often exhibit autocorrelation. By addressing the issue of autocorrelation, the Cochrane–Orcutt estimation helps in obtaining more reliable and accurate estimates of the regression coefficients, leading to better model specification and inference.

Limitations

While the Cochrane–Orcutt procedure is effective in correcting for autocorrelation, it has some limitations. One of the main drawbacks is that it assumes a constant autocorrelation coefficient across all time lags, which may not always be the case in real-world data. Additionally, the procedure requires the selection of an initial model and the convergence of the iterative process, which may not always be straightforward or guaranteed.

See Also

• Autoregressive model
• Durbin–Watson statistic
• Generalized least squares
• Prais–Winsten estimation