Title: Joint modeling of multi-scale time series data using hierarchical hidden Markov models
Authors: Timo Adam - Bielefeld University (Germany) [presenting]
Vianey Leos-Barajas - Bielefeld University (Germany)
Roland Langrock - Bielefeld University (Germany)
Abstract: Hidden Markov models are prevalent in ecology and economics, where they are widely used to model time series data subject to state-switching over time. A basic hidden Markov model comprises an observed state-dependent process that is driven by a hidden state process, the latter of which is typically linked to behavioral modes of an animal (such as resting, foraging or traveling) or economic market regimes (such as recessions or periods of economics growth). To allow for meaningful inference, observations need to be equally spaced in time (or otherwise regularly sampled). However, in animal movement modeling, telemetry sensors often collect data from the same individual at different scales. Typical examples are step lengths obtained from GPS tags every hour, dive depths obtained from time-depth recorders once per dive or accelerations obtained from accelerometers several times per second. Similarly, in economics, stock market data are often collected at a daily (or even finer) scale, whereas macroeconomic indicators are typically observed on a monthly, quarterly or yearly basis. To account for differing temporal resolutions across multiple variables as well as to allow for joint inference at multiple scales, we consider hierarchical hidden Markov models, where the observations are regarded as stemming from several, connected hidden state processes, each of which operates at the scale at which the corresponding variables were observed.