The Finite-Sample Properties of Autoregressive Approximations of Fractionally-Integrated and Non-Invertible Processes
S. D. Grose and D. S. Poskitt
This paper investigates the empirical properties of autoregressive
approximations to two classes of process for which the usual regularity conditions
do not apply; namely the non-invertible and fractionally integrated processes
considered in Poskitt (2006). In that paper the theoretical consequences of
fitting long autoregressions under regularity conditions that allow for these
two situations was considered, and convergence rates for the sample autocovariances
and autoregressive coefficients established. We now consider the finite-sample
properties of alternative estimators of the AR parameters of the approximating
AR(h) process and corresponding estimates of the optimal approximating order
h. The estimators considered include the Yule-Walker, Least Squares,
and Burg estimators.
Keywords: Autoregression, autoregressive approximation, fractional process, non-invertibility, order selection.
