An empirical likelihood goodness-of-fit test for time series

The testing of a computing model for a stationary time series is a standard task in statistics. When a parametric approach is used to model the time series, the question of goodness-of-fit arises. In this paper, we employ the empirical likelihood for an a-mixing process and formulate a statistic test measures the goodness-of-fit of a parametric model. The technique is based on comparison with kernel smoothing estimators. The goodness of- fit test proposed is based on the asymptotics of the empirical likelihood, which has two attractive features. One is its automatic consideration of the variation associated with the nonparametric fit due to the empirical likelihood's ability to studentise internally. The other one is that the asymptotic distributions of the test statistic are free of unknown parameters which avoids secondary plug-in estimation. We apply the empirical likelihood based test to a discretised diffusion model which has been recently considered in financial market analysis.