Model Specification Testing in Nonparametric and Semiparametric Time Series Econometric Models

We propose a simultaneous model specification procedure for the conditional mean and conditional variance in nonparametric and semiparametric time series econometric models. An adaptive and optimal model specification test procedure is then constructed and its asymptotic properties are investigated. The main results extend and generalize existing results for testing the mean of a fixed design nonparametric regression model to the testing of both the conditional mean and conditional variance nonparametric and semiparametric time series econometric models. In addition, we develop computer-intensive bootstrap simulation procedures for the selection of an interval of bandwidth parameters as well as the choice of asymptotic critical values. An example of implementation is given to show how to implement the proposed simultaneous model specification procedure in practice. Moreover, finite sample studies are presented to support the proposed test procedure