Consistent Testing of Functional Form in Time Series Models∗

We develop a consistent procedure for testing the adequacy of parametric time series models. The approach is to extend Herman Bierens’idea of examining the covariances between regression residuals and an exponential weight function, to check the full range of orthogonalities predicted for the score contributions in quasi-maximum likelihood estimation. Tests of this type, which involve nuisance parameters, are constructed as either ‘sup’ed or integrated conditional moment tests, and are often implemented using bootstrap methods. However, our emphasis in this study is on practical implementation. We study a two-statistic approach that aims to exploit the available power while keeping computing requirements to a minimum.