28푡ℎ European Meeting of Statisticians, 2010 Specification Tests for Nonlinear Time Series Models

We propose a new model adequacy test for parametric conditional distributions in nonlinear time series models. These tests are necessary to justify efficient maximum likelihood estimation, to estimate intensity in duration models and downside risk in risk-management, especially on nonlinear portfolios. They can serve also as a density forecast evaluation tool. Uniformity and independence of series obtained by applying the conditional probability integral transform are simultaneously checked by means of continuous functionals of a biparameter process. We establish weak convergence of the empirical process under parameter uncertainty. The test has power against local alternatives converging under the null with a parametric rate and solves consistency problems of previous single parameter tests. We justify a parametric bootstrap approximation that accounts for parameter estimation effects. We extend the test in two directions: higher order joint distributions and more lags are considered. We derive an explicit formula to compute test statistics without numerical integration. Monte Carlo experiments show that the test has a good power against many different alternatives, both in linear and nonlinear dynamic models. We check adequacy of various heteroscedastic models for stock exchange index data