Multi-scale modelling of time series data via hidden Markov models

Fine-scale time series data in ecology can reveal rapid changes in ecosystems, animal movement patterns and behaviors. At the same time, a composition of fine-scale observations can provide information on larger scale patterns, such as an animal migrating vs an animal foraging. These two processes are both evident in the same time series, yet are inferred at different temporal scales. Hidden Markov models (HMMs) are a common class of time series models applied to animal movement and other ecological data. Their ability to connect an observation process to an underlying state process, matches the intuition that what we observe an animal doing stems from its (unobserved) behavior. We can further extend the HMM framework to have multi-scale state processes evolving at different temporal scales to reflect that there are both rapid and slow-changing ecological processes informed by the fine-scale time series data. This extension is referred to as a hierarchical HMM -- more precisely, an HMM with multi-scale state structures. We demonstrate the utility of the hierarchical HMM with applications to tiger shark and killer whale data.