Significance tests and spurious correlation in regression models with autocorrelated errors

In this paper, we report some results on the exact significance level when the usual F-statistic is used in a linear regression model with autocorrelated disturbances. The exact tail area probabilities sometimes differ substantially from the nominal size used in an ‘F-test’ and from upper-bound probabilities derived by Kiviet (1979) which do not depend on the values of the regressors. A similar conclusion is also reached for the exact size of the significance tests for the spurious regressions considered by Granger and Newbold (1974, 1977). The results indicate once more that one has to be careful when using an algebraic F-test in the presence of autoregressive errors. However then too, the Durbin-Watson test is expected to indicate the presence of autocorrelation.