Non-stationary autoregressive processes with infinite variance


Correspondence to: Department of Mathematics, Zhejiang University, Hangzhou, 310027, China.


Consider an AR(p) process inline image, where {ɛt} is a sequence of i.i.d. random variables lying in the domain of attraction of a stable law with index 0<α<2. This time series {Yt} is said to be a non-stationary AR(p) process if at least one of its characteristic roots lies on the unit circle. The limit distribution of the least squares estimator (LSE) of inline image for {Yt} with infinite variance innovation {ɛt} is established in this paper. In particular, by virtue of the result of Kurtz and Protter (1991) of stochastic integrals, it is shown that the limit distribution of the LSE is a functional of integrated stable process. Simulations for the estimator of β and its limit distribution are also given.