A simple message for autocorrelation correctors: don't

Though the practice of ‘correcting for residual autocorrelation’ has long been critized, it is still commonly advocated and followed. A simple example shows that even when a linear regression model has first-order autoregressive errors, it is possible for autoregressive least squares estimation (e.g., Cochrane-Orcutt) to yield inconsistent estimates. This dramatically illustrates that ‘autocorrelation correction’ is invalid in general, and cannot be justified on the grounds of ‘robustifying’ estimation against the presence of residual serial correlation. Invalid common factors in I(1) systems also have adverse effects on inference. A ‘general-to-specific’ modelling strategy applied to the observed modelled variables avoids these difficulties