Asymptotics for LS, GLS, and Feasible GLS Statistics in an AR(1) Model with Conditional Heteroskedaticity

47 Pages Posted: 9 Jun 2008

See all articles by Donald W. K. Andrews

Donald W. K. Andrews

Yale University - Cowles Foundation

Patrik Guggenberger

Pennsylvania State University, College of the Liberal Arts - Department of Economic

Date Written: June 2008

Abstract

This paper considers 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 and the distribution of the time series of innovations. In particular, we consider the full range of cases in which the autoregressive parameter rho_n satisfies (i) n(1 - rho_n) -> infinity and (ii) n(1 - rho_n) -> h_1 < infinity as n -> infinity, 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.

Keywords: Asymptotic distribution, Autoregression, Conditional heteroskedasticity, Generalized least squares, Least squares

JEL Classification: C22

Suggested Citation

Andrews, Donald W. K. and Guggenberger, Patrik, Asymptotics for LS, GLS, and Feasible GLS Statistics in an AR(1) Model with Conditional Heteroskedaticity (June 2008). Cowles Foundation Discussion Paper No. 1665, Available at SSRN: https://ssrn.com/abstract=1142834

Donald W. K. Andrews (Contact Author)

Yale University - Cowles Foundation ( email )

Box 208281
New Haven, CT 06520-8281
United States
203-432-3698 (Phone)
203-432-6167 (Fax)

Patrik Guggenberger

Pennsylvania State University, College of the Liberal Arts - Department of Economic ( email )

524 Kern Graduate Building
University Park, PA 16802-3306
United States

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