Asymptotic results of error density estimator in nonlinear autoregressive models

This paper considers the asymptotic properties of the error density estimator in the nonlinear autoregressive models with \(\alpha\) $\alpha$ -mixing errors. The asymptotic distribution and uniform convergence rate for the kernel density estimator of error density function are obtained. Last, some simulations of histograms, confidence intervals and mean integrated square errors are illustrated, which agree with our theoretical results.