Hidden Markov Mixture Autoregressive Models: Stability and Moments

Details Hidden Markov Mixture Autoregressive Models: Stability and Moments Hidden Markov Mixture Autoregressive Models: Stability and Moments

2011-05-06

arxiv.org/abs/1105.1212v2

Mathematics

Statistics Theory

22 pages

Scientific paper

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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