The Effect of the Estimation on Goodness-of-Fit Tests in Time Series Models

We analyze, by simulation, the finite-sample properties of goodness-of-fit tests based on residual autocorrelation coefficients (simple and partial) obtained using different estimators frequently used in the analysis of autoregressive moving-average time-series models. The estimators considered are unconditional least squares, maximum likelihood and conditional least squares. The results suggest that although the tests based on these estimators are asymptotically equivalent for particular models and parameter values, their sampling properties for samples of the size commonly found in economic applications can differ substantially, because of differences in both finite-sample estimation efficiencies and residual regeneration methods.