Limiting distributions for explosive PAR(1) time series with strongly mixing innovation

Dominique Dehay

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arXiv · 1501.02151

Limiting distributions for explosive PAR(1) time series with strongly mixing innovation

Dominique Dehay

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Abstract

This work deals with the limiting distribution of the least squares estimators of the coefficients a r of an explosive periodic autoregressive of order 1 (PAR(1)) time series X r = a r X r--1 +u r when the innovation {u k } is strongly mixing. More precisely {a r } is a periodic sequence of real numbers with period P \textgreater{} 0 and such that P r=1 |a r | \textgreater{} 1. The time series {u r } is periodically distributed with the same period P and satisfies the strong mixing property, so the random variables u r can be correlated.

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Dominique Dehay. 2015-01-09. Limiting distributions for explosive PAR(1) time series with strongly mixing innovation. https://arxiv.org/abs/1501.02151

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