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Keywords:

  • AR(p);
  • infinite variance;
  • nonstationary;
  • stable processes;
  • stochastic integrals
  • Primary 62M10;
  • 62E20;
  • Secondary 60F17

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.