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December 2019 Statistical inference for autoregressive models under heteroscedasticity of unknown form
Ke Zhu
Ann. Statist. 47(6): 3185-3215 (December 2019). DOI: 10.1214/18-AOS1775

Abstract

This paper provides an entire inference procedure for the autoregressive model under (conditional) heteroscedasticity of unknown form with a finite variance. We first establish the asymptotic normality of the weighted least absolute deviations estimator (LADE) for the model. Second, we develop the random weighting (RW) method to estimate its asymptotic covariance matrix, leading to the implementation of the Wald test. Third, we construct a portmanteau test for model checking, and use the RW method to obtain its critical values. As a special weighted LADE, the feasible adaptive LADE (ALADE) is proposed and proved to have the same efficiency as its infeasible counterpart. The importance of our entire methodology based on the feasible ALADE is illustrated by simulation results and the real data analysis on three U.S. economic data sets.

Citation

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Ke Zhu. "Statistical inference for autoregressive models under heteroscedasticity of unknown form." Ann. Statist. 47 (6) 3185 - 3215, December 2019. https://doi.org/10.1214/18-AOS1775

Information

Received: 1 April 2018; Revised: 1 August 2018; Published: December 2019
First available in Project Euclid: 31 October 2019

Digital Object Identifier: 10.1214/18-AOS1775

Subjects:
Primary: 62F03 , 62F12 , 62F35 , 62M10

Keywords: Adaptive estimator , autoregressive model , conditional heteroscedasticity , Heteroscedasticity , weighted least absolute deviations estimator , wild bootstrap

Rights: Copyright © 2019 Institute of Mathematical Statistics

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Vol.47 • No. 6 • December 2019
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