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

Abstract

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 Horváth and Zitikis (2003) to nonlinear autoregressive models.