Asymptotic normality of residual density estimator in stationary and explosive autoregressive models

The error density estimator in the first-order autoregressive model is considered based on alpha-mixing errors. Since the errors are not observed, the residual kernel density estimator is provided. The asymptotic normality of the residual estimator is obtained when the autoregressive model is a stationary process or an explosive process. Moreover, some simulations such as the fitted curves, mean integrated square errors and histograms are illustrated to the residual kernel estimator and residual histogram estimator. It is shown that the residual kernel estimator with smooth kernel is smoother than the residual histogram estimator. (C) 2022 Elsevier B.V. All rights reserved.