Asymptotic Theory for M-Estimates in Unstable AR(p) Processes with Infinite Variance Innovations
Abstract
In this paper, we present the asymptotic distribution of M-estimators for parameters in non-stationary AR(p) processes. The innovations are assumed to be in the domain of attraction of a stable law with index 0<α2. In particular, when the model involves repeated unit roots or conjugate complex unit roots, M-estimators have a higher asymptotic rate of convergence compared to the least square estimators and the asymptotic results can be written as It\o stochastic integrals.
0