Bulletin of the
Korean Mathematical Society BKMS

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Bull. Korean Math. Soc. 2006; 43(4): 813-820

Printed December 1, 2006

Copyright © The Korean Mathematical Society.

Stationarity and $\beta$-mixing property of a mixture AR-ARCH models

Oesook Lee

Ewha Womans University

Abstract

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We consider a MAR model with ARCH type conditional heteroscedasticity. MAR-ARCH model can be derived as a smoothed version of the double threshold AR-ARCH model by adding a random error to the threshold parameters. Easy to check sufficient conditions for strict stationarity, $\beta$-mixing property and existence of moments of the model are given via Markovian representation technique.

Keywords: mixture AR-ARCH model, Markov chain, stationarity, geometric ergodicity, $\beta$-mixing

MSC numbers: 62M10, 60J10

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