A Functional Central Limit Theorem for an ARMA(p, q) Process with Markov Switching

Abstract

Abstract In this paper, we give a tractable sufficient condition for functional central limit theorem to hold in Markovswitching ARMA ( p , q ) model.Keywords: Functional central limit theorem, Markov switching ARMA ( p , q ) process, φ -mixing. 1. Introduction SincetheseminalworkofHamilton(1989),nonlineartimeseriesmodelssubjecttoMarkovswitchingarewidelyusedformodellingdynamicsindifferentfields, especiallyineconometricstudies(Krolzig,1997; Hamilton and Raj, 2002). Markov switching autoregressive moving average(MSARMA)( p , q )model, in which a hidden Markov process governs the behavior of an observable time series, exhibitsstructural breaks and local linearity. When we consider a time series model as a data generating pro-cess, one of the important properties to show is the (functional) central limit theorem. Functionalcentral limit theorem(FCLT) is applied for statistical inference in time series to establish the asymp-totics of various statistics concerning, for example a test for stability such as CUCUM or MOSUMand unit root testing. Probabilistic properties of MSARMA(