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

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.