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

TL;DR

This paper investigates the limiting distribution of least squares estimators in explosive periodic autoregressive (PAR(1)) time series with strongly mixing, possibly correlated innovations, extending understanding of estimator behavior in complex dependent settings.

Contribution

It provides new theoretical results on the asymptotic distribution of estimators for explosive PAR(1) models with strongly mixing innovations, a less explored dependence structure.

Findings

Derived the limiting distribution for estimators in explosive PAR(1) models

Extended analysis to strongly mixing, correlated innovations

Established conditions under which the asymptotic results hold

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.