Non‐stationary autoregressive processes with infinite variance
Анотація
Consider an AR( p ) process , where { ɛ 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 for { Y t } with infinite variance innovation { ɛ 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.
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