Hidden Markov Mixture Autoregressive Models: Stability and Moments

TL;DR

This paper presents a novel hidden Markov mixture autoregressive model with stability analysis, moment derivations, and a dynamic programming forecasting algorithm, validated through simulations and forecasting applications.

Contribution

It introduces a new mixture autoregressive model with hidden Markov structure, providing stability, moment analysis, and an efficient forecasting algorithm.

Findings

Derived the limiting behavior of the first moment.

Established bounds for the variance's long-term behavior.

Demonstrated model efficacy through simulations and forecasting.

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.