Hidden Markov Mixture Autoregressive Models: Stability and Moments

Abstract

This article introduces a parsimonious structure for mixture of autoregressive models, where the weighting coefficients are determined through latent random variables, as functions of all past observations. These latent variables follow a Markov model. We propose a dynamic programming algorithm for forecasting, which reduces the volume of calculations. We also derive limiting behavior of unconditional first moment of the process and an appropriate upper bound for the limiting value of the variance. Further more, we show convergence and stability of the second moment. Finally, we illustrate the efficacy of the proposed model by simulation.

Keywords:

• Dynamic programming
• Forecasting
• Hidden Markov Model
• Mixture autoregressive Model
• Stability

Mathematics Subject Classification:

• Primary 62M10
• 60J10. Secondary 60G25

View correction statement:

Corrigendum

Acknowledgments

The authors would like to express their thanks to both anonymous referees for valuable comments and suggestions which improved the original manuscript. This research was in part supported by a grant from IPM (No. 89600124).