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In this paper, we present the asymptotic distribution of M-estimators forparameters in non-stationary AR(p) processes. The innovations are assumed to bein the domain of attraction of a stable law with index $0<\alpha\le2$. Inparticular, when the model involves repeated unit roots or conjugate complexunit roots, M-estimators have a higher asymptotic rate of convergence comparedto the least square estimators and the asymptotic results can be written asIt\^{o} stochastic integrals.

Asymptotic Theory for M-Estimates in Unstable AR(p) Processes with Infinite Variance Innovations