Statistical inference for autoregressive models under heteroscedasticity of unknown form

TL;DR

This paper develops a comprehensive inference framework for autoregressive models with unknown heteroscedasticity, including estimators, covariance estimation, and model checking, validated through simulations and real data.

Contribution

It introduces a feasible adaptive LADE and a complete inference procedure for heteroscedastic autoregressive models of unknown form.

Findings

Asymptotic normality of weighted LADE established

RW method effectively estimates covariance matrix

Method performs well on real U.S. economic data

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.