Asymptotic theory for M-estimates in unstable AR(p) processes with infinite variance innovations

In this paper, we present the asymptotic distribution of M-estimates for parameters in unstable AR(p) processes. The innovations are assumed to be in the domain of attraction of a symmetric stable law with index 0<α≤2. In particular, in the case of repeated unit roots or conjugate complex unit roots, M-estimates have a higher asymptotic rate of convergence compared to the least square estimates and the asymptotic results can be written as Itô stochastic integrals.