Asymptotics for LS, GLS, and feasible GLS statistics in an AR(1) model with conditional heteroskedasticity

Donald W.K. Andrews, Patrik Guggenberger

Research output: Contribution to journalArticle

9 Scopus citations

Abstract

We consider a first-order autoregressive model with conditionally heteroskedastic innovations. The asymptotic distributions of least squares (LS), infeasible generalized least squares (GLS), and feasible GLS estimators and t statistics are determined. The GLS procedures allow for misspecification of the form of the conditional heteroskedasticity and, hence, are referred to as quasi-GLS procedures. The asymptotic results are established for drifting sequences of the autoregressive parameter ρn and the distribution of the time series of innovations. In particular, we consider the full range of cases in which ρn satisfies n(1- ρn)→∞ and n(1- ρn)→ h1∈[0,∞) as n→∞, where n is the sample size. Results of this type are needed to establish the uniform asymptotic properties of the LS and quasi-GLS statistics.

Original languageEnglish (US)
Pages (from-to)196-210
Number of pages15
JournalJournal of Econometrics
Volume169
Issue number2
DOIs
StatePublished - Aug 1 2012

All Science Journal Classification (ASJC) codes

  • Economics and Econometrics

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