Non-detection of the serial correlation in least squares regression; frequency and consequences

The robustness and efficiency of OLS statistical inference is assessed in cases where the disturbances are serially correlated. In addition the frequency of accepting independence of the disturbances (and thus the acceptance of OLS results) is considered. An attainable lower bound for the probability of a type two error in testing for serial correlation is established. Case studies indicate that confidence regions for regression coefficients are very sensitive to departures from independence of the disturbances; OLS prediction appears to be more robust. When the sample is small, non-detection of serial correlation will frequently occur. These results suggest a tentative strategy for the detection of serial correlation.