Simultaneous Diagnostic Testing for Nonlinear Time Series Models with An Application to the U.S. Federal Fund Rate

Abstract This paper proposes a simultaneous test for the specification of the conditional mean and conditional variance functions as well as the error distribution in nonlinear time series models. Constructed by comparing two density estimators for the response variable, the proposed test has a Gumbel‐limiting distribution under the null hypothesis and is consistent against a general class of alternative hypotheses. A parametric bootstrap procedure is proposed for practical implementation, and is shown to perform well in extensive simulations. The application to the continuous time diffusion model is illustrated via an analysis on the U.S. Federal fund rate data.