On the geometric ergodicity of the mixture autoregressive model

Geometric ergodicity is very useful in establish-ing mixing conditions and central limit results for parameterestimates of a model. It also justifies the use of laws of largenumbers and forms part of the basis for exploring the asymptotictheory of a model.The class of mixture autoregressive (MAR) models provides aflexible way to model various features of time series data and iswell suited for density forecasting. The MAR models are ableto capture many stylised properties of real data, such as multi-modality, asymmetry and heterogeneity. We show here that theMAR model is geometrically ergodic and by implication satisfiesthe absolutely regular and strong mixing conditions.