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ON MARKOV-SWITCHING ARMA PROCESSES—STATIONARITY, EXISTENCE OF MOMENTS, AND GEOMETRIC ERGODICITY

Published online by Cambridge University Press:  01 February 2009

Robert Stelzer
Robert Stelzer*
Affiliation:
Technische Universität München
*
*Address correspondence to Robert Stelzer, Zentrum Mathematik, Technische Universität München, Boltzmannstraße 3, D-85747 Garching, Germany; e-mail: [email protected].
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Abstract

The probabilistic properties of ℝd-valued Markov-switching autoregressive moving average (ARMA) processes with a general state space parameter chain are analyzed. Stationarity and ergodicity conditions are given, and an easy-to-check general sufficient stationarity condition based on a tailor-made norm is introduced. Moreover, it is shown that causality of all individual regimes is neither a necessary nor a sufficient criterion for strict negativity of the associated Lyapunov exponent.

Finiteness of moments is also considered and geometric ergodicity and strong mixing are proven. The easily verifiable sufficient stationarity condition is extended to ensure these properties.

Type
ARTICLES
Information
Econometric Theory , Volume 25 , Issue 1 , February 2009 , pp. 43 - 62
Copyright
Copyright © Cambridge University Press 2009

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