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Abstract:  Hidden Markov models (HMMs) are commonly used to identify latent processes from observed time series, but it is challenging to fit them to large and complex time series collected by modern sensors. Using data from threatened resident killer whales (Orcinus orca) off the western coast of Canada as a case study, we provide solutions to three common challenges faced when identifying latent behaviour from complicated biologging data. First, biologging time series often violate common assumptions of HMMs when collected at high frequencies. We thus propose a hierarchical approach which utilizes moving-window Fourier analysis to capture fine-scale dependence structures. Second, modern technology allows researchers to directly label the latent process of interest, but rare labels can have a negligible influence on parameter estimates. We introduce a weighted likelihood approach that increases the relative influence of labelled observations. Third, applying HMMs to large time series is computationally demanding, so we propose a novel EM algorithm that combines a partial E step with variance-reduced stochastic optimization within the M step. These solutions allow researchers to model biologging data with HMMs that are more interpretable, accurate, and efficient to fit than existing methods.