Modelling multi-scale state-switching functional data with hidden Markov models

TL;DR

This paper introduces a hierarchical hidden Markov model approach for analyzing high-frequency, multi-scale functional data with complex dependence structures, demonstrated through a case study on whale movement.

Contribution

It presents a novel hierarchical modeling framework combining HMMs with fine-scale models for complex functional data analysis.

Findings

More interpretable state estimation

More accurate parameter estimates

Applicable to various sequences of curves

Abstract

Data sets comprised of sequences of curves sampled at high frequencies in time are increasingly common in practice, but they can exhibit complicated dependence structures that cannot be modelled using common methods of Functional Data Analysis (FDA). We detail a hierarchical approach which treats the curves as observations from a hidden Markov model (HMM). The distribution of each curve is then defined by another fine-scale model which may involve auto-regression and require data transformations using moving-window summary statistics or Fourier analysis. This approach is broadly applicable to sequences of curves exhibiting intricate dependence structures. As a case study, we use this framework to model the fine-scale kinematic movement of a northern resident killer whale (Orcinus orca) off the coast of British Columbia, Canada. Through simulations, we show that our model produces more interpretable state estimation and more accurate parameter estimates compared to existing methods.