A goodness-of-fit test of the errors in nonlinear autoregressive time series models

This paper considers the problem of fitting an error density to the goodness-of-fit test of the errors in a nonlinear autoregressive stationary time series regression model. The test statistic is based on the integrated squared error of the nonparametric error density estimate and the null error density. Without knowing the nonlinear autoregressive function, we can show that the test statistic behaves asymptotically the same as the one based on the true errors.