STATISTICAL INFERENCE FOR AUTOREGRESSIVE MODELS UNDER HETEROSCEDASTICITY OF UNKNOWN FORM

• 成果类型: Article
• 署名作者: Zhu, Ke
• 署名单位: University of Hong Kong
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/18-AOS1775
• 发表日期: 2019
• 页码: 3185-3215
• 关键词: time-series; CONDITIONAL HETEROSCEDASTICITY; efficient estimation; arma models; variance; regression; heteroskedasticity; volatility; tests; nonstationarities

摘要

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.