M-estimation For Nonstationary AR(p)processes With Heavy-tailed Distribution

In this thesis,we consider the asymptotic properties of M-estimation for parameters in nonstationary AR(p)processes with nonzero location parameter when estimating the location parameter simultaneously with autoregressive coefficients.The innovations are assumed to be i.i.d.random variables in the domain attraction of a stable law with index 0 < ? < 2.A lot of work has been done previously on M-estimation of general AR(p)processes.Davis et al.(1992)studied the asymptotic properties of Mestimation and LAD estimation for general nonstationary AR(p)processes.Chan and Zhang(2012)obtained the limiting distribution for the LS estimation of the parameters for nonstationary AR(p)processes with infinite variance innovations.Sohrabi and Zarepour(2019)conducted extensive research on the nonstationary AR(p)process with infinite variance innovations.In this paper,we extend the above conclusions.Under the condition of infinite variance,it may not be necessarily trivial to assume that the location parameter is zero.We will use the M-estimation to estimate the location parameter simultaneously with the autoregressive coefficients,and then study the asymptotic properties of the Mestimation.We will show that the limit distribution of the M-estimation is a functional of integrated stable process.