Bayesian Hidden Markov Modelling Using Circular-Linear General Projected Normal Distribution

TL;DR

This paper presents a Bayesian hidden Markov model that jointly analyzes circular and linear time-series data using a flexible distribution, relaxing independence assumptions to improve modeling accuracy.

Contribution

It introduces a novel multivariate HMM with a general projected normal distribution, allowing for skewed and bimodal cluster-specific distributions and dependence between components.

Findings

Successfully recovers hidden structures in simulated data

Effectively models wind speed and direction data

Demonstrates improved fit over models assuming independence

Abstract

We introduce a multivariate hidden Markov model to jointly cluster time-series observations with different support, i.e. circular and linear. Relying on the general projected normal distribution, our approach allows for bimodal and/or skewed cluster-specific distributions for the circular variable. Furthermore, we relax the independence assumption between the circular and linear components observed at the same time. Such an assumption is generally used to alleviate the computational burden involved in the parameter estimation step, but it is hard to justify in empirical applications. We carry out a simulation study using different data-generation schemes to investigate model behavior, focusing on well recovering the hidden structure. Finally, the model is used to fit a real data example on a bivariate time series of wind speed and direction.