Hidden Markov Mixture Autoregressive Models: Stability and Moments

2011/05/06 by S. H. Alizadeh, Alizadeh, S. H., S. Rezakhah +1
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #FOS: Mathematics #Fuzzy Systems and Optimization #Statistical Methods and Inference #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1105.1212

openalex publication_date 2011/05/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper introduces a new parsimonious structure for mixture of autoregressive models. the weighting coefficients are determined through latent random variables, following a hidden Markov model. We propose a dynamic programming algorithm for the application of forecasting. We also derive the limiting behavior of unconditional first moment of the process and an appropriate upper bound for the limiting value of the variance. This can be considered as long run behavior of the process. Finally we show convergence and stability of the second moment. Further, we illustrate the efficacy of the proposed model by simulation and forecasting.

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