# The conditionally autoregressive hidden Markov model (CarHMM): Inferring behavioural states from animal tracking data exhibiting conditional autocorrelation

## TL;DR

This paper introduces the CarHMM, a novel extension of the hidden Markov model designed to better analyze animal movement data exhibiting conditional autocorrelation, with practical guidelines and biological interpretations.

## Contribution

The paper develops the CarHMM, addressing limitations of traditional HMMs by modeling conditional autocorrelation in animal movement data, and provides comprehensive analysis guidelines.

## Key findings

- CarHMM effectively models conditional autocorrelation in movement data.
- Guidelines for data preprocessing, model selection, and checking are provided.
- Interpretation of behavioral states in biological terms is enhanced.

## Abstract

One of the central interests of animal movement ecology is relating movement characteristics to behavioural characteristics. The traditional discrete-time statistical tool for inferring unobserved behaviours from movement data is the hidden Markov model (HMM). While the HMM is an important and powerful tool, sometimes it is not flexible enough to appropriately fit the data. Data for marine animals often exhibit conditional autocorrelation, self-dependence of the step length process which cannot be explained solely by the behavioural state, which violates one of the main assumptions of the HMM. Using a grey seal track as an example, along with multiple simulation scenarios, we motivate and develop the conditionally autoregressive hidden Markov model (CarHMM), which is a generalization of the HMM designed specifically to handle conditional autocorrelation. In addition to introducing and examining the new CarHMM, we provide guidelines for all stages of an analysis using either an HMM or CarHMM. These include guidelines for pre-processing location data to obtain deflection angles and step lengths, model selection, and model checking. In addition to these practical guidelines, we link estimated model parameters to biologically meaningful quantities such as activity budget and residency time. We also provide interpretations of traditional "foraging" and "transiting" behaviours in the context of the new CarHMM parameters.