COWLES FOUNDATION FOR RESEARCH IN
ECONOMICS Box 208281
COWLES FOUNDATION DISCUSSION PAPER NO. 1665RR Asymptotics for LS, GLS, and Feasible GLS Statistics Donald W.K. Andrews and Patrik Guggenberger June 2008 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. |
