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Over the last decade, hidden Markov models (HMMs) have become increasinglypopular in statistical ecology, where they constitute natural tools forstudying animal behavior based on complex sensor data. Corresponding analysessometimes explicitly focus on - and in any case need to take into account -periodic variation, for example by quantifying the activity distribution overthe daily cycle or seasonal variation such as migratory behavior. For HMMsincluding periodic components, we establish important mathematical propertiesthat allow for comprehensive statistical inference related to periodicvariation, thereby also providing guidance for model building and modelchecking. Specifically, we derive the periodically varying unconditional statedistribution as well as the time-varying and overall state dwell-timedistributions - all of which are of key interest when the inferential focuslies on the dynamics of the state process. We use the associated novelinference and model-checking tools to investigate changes in the diel activitypatterns of fruit flies in response to changing light conditions.

Inference on the state process of periodically inhomogeneous hidden Markov models for animal behavior