Specification Tests for Nonlinear Time Series Models

This paper proposes a new parametric model adequacy test for possibly nonlinear time series models such as generalized autoregressive conditional heteroskedasticity (GARCH) and autoregressive conditional duration (ACD). We consider the correct specification of parametric conditional distributions, not only some particular conditional characteristics. Using the true parametric conditional distribution under the null hypothesis we transform data to uniform iid series. The uniformity and serial independence of these transformed series is then examined simultaneously by comparing joint empirical distribution functions with the product of its theoretical uniform marginals by means of Cramer-von Mises or Kolmogorov-Smirnov statistics. We study consistency and asymptotic properties of such tests taking into account parameter estimation effect. Since asymptotic distribution is case dependent, critical values can not be tabulated and we use a bootstrap approximation. The test analyzed in this paper can be extended to in two ways: higher order joint distributions and more lags could be considered. The performance of the test is compared with classical specification checks when estimating ACD models.