CFDP 1665R2

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


Publication Date: June 2008

Revision Date: February 2012

Pages: 55


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 ρn satisfies (i) n(1 - ρn) → ∞ and (ii) n(1 - ρn) approaches h1 in [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.


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

JEL Classification Codes:  C22

See CFP: 1365