Asymptotics of theLp-Norms of Density Estimators in the Nonlinear Autoregressive Models

This article investigates the asymptotic behavior of the error density function in nonlinear autoregressive stationary time series regression models. For any 1 ⩽ p < ∞, the kernel density estimator of residuals is shown to be consistent for the error estimator concerning the Lp-distance, which extends the result developed by Cheng and Sun (2008) in L2-norm. Moreover, the result developed in this article is extended the results of Horvath and Zitikis (2003) to nonlinear autoregressive models.