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Non‐stationary autoregressive processes with infinite variance
Author(s) -
Chan Ngai Hang,
Zhang Rongmao
Publication year - 2012
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/j.1467-9892.2012.00807.x
Subject(s) - mathematics , autoregressive model , limit (mathematics) , estimator , stationary sequence , series (stratigraphy) , distribution (mathematics) , asymptotic distribution , stationary process , central limit theorem , unit circle , sequence (biology) , domain (mathematical analysis) , mathematical analysis , stochastic process , statistics , paleontology , biology , genetics
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.