Hypothesis testing based on goodness-of-fit in the moving average time series model

Small sample properties of t-tests are compared with those of tests based on relative goodness- of-fit in the context of the first order moving average time series model. Monte Carlo experiments reported in the paper suggest that the actual size of these t-tests greatly exceeds theoretical large sample significance levels, while conformity of goodness-of-fit statistics to the appropriate chi-square or F-distributions is much closer. The evidence presented suggests that practitioners are well advised to employ goodness-of-fit tests as a check on results of t-tests particularly when the latter indicate ‘significance’.