Stationarity and β-mixing property of a mixture AR-ARCH models

Abstract

We consider a MAR model with ARCH type conditional heteroscedasticity. NIAR-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. 3-mixing property and existence of moments of the model are given via Markovian representation technique.