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 Stationarity and $\beta$-mixing property of a mixture AR-ARCH models Bull. Korean Math. Soc. 2006 Vol. 43, No. 4, 813-820 Printed December 1, 2006 Oesook Lee Ewha Womans University Abstract : 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 Downloads: Full-text PDF