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On stability of nonlinear AR processes with Markov switching

Part of: Inference from stochastic processes Markov processes

Published online by Cambridge University Press:  01 July 2016

J.-F. Yao  and
J.-G. Attali
J.-F. Yao*
Affiliation:
SAMOS, Université Paris 1
J.-G. Attali*
Affiliation:
Université Paris 6 and SAMOS, Université Paris 1
*
∗ Postal address: SAMOS, Université Paris 1, 90, rue de Tolbiac, F-75634 Paris cedex 13, France. Email address: [email protected]
∗∗ Postal address: Labo. de Probabilités, Université Paris 6, 4, place Jussieu, F-75252 Paris cedex 05, France.
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Abstract

We investigate the stability problem for a nonlinear autoregressive model with Markov switching. First we give conditions for the existence and the uniqueness of a stationary ergodic solution. The existence of moments of such a solution is then examined and we establish a strong law of large numbers for a wide class of unbounded functions, as well as a central limit theorem under an irreducibility condition.

Keywords

Markov switchingnonlinear ARLyapounov functionsstability

MSC classification

Primary: 60J20: Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.)
Secondary: 62M10: Time series, auto-correlation, regression, etc.
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 32 , Issue 2 , June 2000 , pp. 394 - 407
Copyright
Copyright © Applied Probability Trust 2000 

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