Sequential predictive e-diagnostics for hidden Markov models of animal movement

Hidden Markov models are standard for inferring behavioural states from animal movement data, but checking whether a fitted latent-state model predicts held-out movement well remains difficult. We develop sequential predictive e-diagnostics that evaluate a fitted movement HMM as a generator of validation trajectories. Each diagnostic specifies a predictable alternative density, and its ratio to the fitted models observable one-step predictive density defines an e-value increment. The denominator is obtained by filtering over latent states, not by conditioning on a decoded path. Under a fixed train/validation protocol, the cumulative product is an e-process, giving anytime-valid thresholds under optional stopping and predictable switching. The construction extends to weighted and state-localized evidence, feature-level circular-linear checks, and blockwise summaries. Controlled simulations show calibration under the fitted-generator null and sensitivity to targeted misspecifications. A leave-one-animal-out elk case study illustrates pooled, individual-specific and state-localized predictive model criticism in a standard movement-HMM workflow.