  In this work we deal with the problem of fitting an error density to the
goodness-of-fit test of the errors in nonlinear autoregressive time series
models with stationary $\alpha$-mixing error terms. The test statistic is based
on the integrated squared error of the nonparametric error density estimate and
the null error density. By deriving the asymptotic normality of test statistics
in 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 more
general case.
