Box-Cox Estimation with Standard Econometric Problems

Savin and White (1978) indicated a way to combine the Box-Cox (1964) test with autoregressive disturbances. That work is extended to indicate how to implement: 1. the standard Box-Cox test, 2. the Box-Cox test in the presence of autocorrelation, and 3. the Box-Cox test in the presence of heteroscedasticity. Different forms of the test can be implemented with standard computer programs capable of performing ordinary least squares, weighted least squares, and a maximum likelihood autoregressive estimation, such as in Beach and MacKinnon (1978). There seems to be no reason why the Box-Cox test should not be used in conjunction with analogous variations of the standard model when there is evidence of autocorrelation or heteroscedasticity. Failure to correct for heteroscedasticity can give misleading results.