Sequential Bayesian Learning for Hidden Semi-Markov Models

TL;DR

This paper introduces an efficient Bayesian method for sequential parameter estimation in Hidden Semi-Markov Models, addressing computational challenges and enabling real-time analysis for applications like financial time series.

Contribution

It develops a novel computational scheme for exact Bayesian estimation of HSMMs that is feasible for sequential data analysis, improving upon existing batch methods.

Findings

Efficient Bayesian estimation scheme verified for HSMMs.

Demonstrated application to VIX time series for regime detection.

Showed potential for model selection and clustering in financial data.

Abstract

In this paper, we explore the class of the Hidden Semi-Markov Model (HSMM), a flexible extension of the popular Hidden Markov Model (HMM) that allows the underlying stochastic process to be a semi-Markov chain. HSMMs are typically used less frequently than their basic HMM counterpart due to the increased computational challenges when evaluating the likelihood function. Moreover, while both models are sequential in nature, parameter estimation is mainly conducted via batch estimation methods. Thus, a major motivation of this paper is to provide methods to estimate HSMMs (1) in a computationally feasible time, (2) in an exact manner, i.e. only subject to Monte Carlo error, and (3) in a sequential setting. We provide and verify an efficient computational scheme for Bayesian parameter estimation on HSMMs. Additionally, we explore the performance of HSMMs on the VIX time series using Autoregressive (AR) models with hidden semi-Markov states and demonstrate how this algorithm can be used for regime switching, model selection and clustering purposes.