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

Donald Andrews (donald.andrews@yale.edu) and Patrik Guggenberger

No 1665R2, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

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}) approaches infinity and (ii) n(1 - rho_{n}) approaches h_{1} in [0,infinity) as n approaches 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 (search for similar items in EconPapers)
JEL-codes: C22 (search for similar items in EconPapers)
Pages: 55 pages
Date: 2008-06, Revised 2012-02
Note: CFP 1365
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (6)

Published in Journal of Econometrics (August 2012), 169(2): 196-210

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Related works:
Journal Article: Asymptotics for LS, GLS, and feasible GLS statistics in an AR(1) model with conditional heteroskedasticity (2012)
Working Paper: Asymptotics for LS, GLS, and Feasible GLS Statistics in an AR(1) Model with Conditional Heteroskedaticity (2010)
Working Paper: Asymptotics for LS, GLS, and Feasible GLS Statistics in an AR(1) Model with Conditional Heteroskedaticity (2008)
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