A goodness-of-fit test of the errors in nonlinear autoregressive time series models with stationary $\alpha$-mixing error terms

摘要

In this work we deal with the problem of fitting an error density to thegoodness-of-fit test of the errors in nonlinear autoregressive time seriesmodels with stationary $\alpha$-mixing error terms. The test statistic is basedon the integrated squared error of the nonparametric error density estimate andthe null error density. By deriving the asymptotic normality of test statisticsin these models, we extend the result of Cheng and Sun (Statist. Probab. Lett.\textbf{78}, 1(2008), 50-59) in the model with i.i.d error terms to the moregeneral case.