# STATIONARITY AND β-MIXING PROPERTY OF A MIXTURE AR-ARCH MODELS

• Lee, Oe-Sook (DEPARTMENT OF STATISTICS, EWHA WOMANS UNIVERSITY)
• Published : 2006.11.30

#### 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.

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#### Cited by

1. Mixtures of autoregressive-autoregressive conditionally heteroscedastic models: semi-parametric approach vol.41, pp.2, 2014, https://doi.org/10.1080/02664763.2013.839129