Non-stationary autoregressive processes with infinite variance

摘要

Consider an AR(p) process Y_t = β,_1Y_(t-1) + … + β_pY_(t-p) + ε_t, where {ε_t} 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 (Y_t} 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 β = (β_1,..., β_p)~T for (Y_t} with infinite variance innovation (ε_t) 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.