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

Min Gao, Wenzhi Yang, Shipeng Wu and Wei Yu

Computational Statistics & Data Analysis, 2022, vol. 175, issue C

Abstract: The error density estimator in the first-order autoregressive model is considered based on α-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.

Keywords: Residual kernel density estimator; Asymptotic distribution; Explosive autoregressive model; α-mixing sequence (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:175:y:2022:i:c:s0167947322001293

DOI: 10.1016/j.csda.2022.107549

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