In this thesis I investigate the application of various statistical approaches towards analysing time series data collected using GPS collars placed on three ungulate species in the same region of the Kruger National Park, South Africa. Animal movement tracking is a rapidly advancing area of ecological research and large datasets are being collected with GPS locations of the animal, with shorter periods between successive locations. A statistical challenge is to segment the movement paths into groups which correspond to different behavioural activities. The aim of my study was to investigate and compare alternative statistical approaches for analysing GPS data and to establish the best statistical framework for interpreting these large herbivore movements. The focus was on which methods are the most appropriate for these animals and the comparison of the movement patterns across species and season. Independent Mixture, Hidden Markov and Bayesian State-Space Models were used to analyse the hourly and daily movements of sable antelope, buffalo and zebra. Mixture Models provide a basic clustering technique to segment the movement paths and identify different underlying groups within the data assumed to correspond to different behavioural states. Posterior probabilities of group membership are used to allocate movements between successive locations to different states. This method ignores the dependence between successive movements. Hidden Markov models (HMMs) use a time series technique and include a dependency between successive observations via a Markov process. Extensions to the HMMs were applied to allow for the inclusion of seasonal covariates and irregular time gaps between successive observations caused by missing locations. A Bayesian state-space model fits a random walk using MCMC methods. The results were very similar to the HMMs but were more challenging to fit and required much more processing time. In the absence of informative prior information, the Bayesian method does not provide any improvement on the HMMs. The HMMs perform slightly better in terms of state allocation accuracy than the Mixture Models. However Mixture Models perform acceptably if only a straightforward clustering of the observations is required. However, if a more robust method is required, the HMMs are relatively easy to fit and extend, allow for investigation of the state switching probabilities and are recommended as the best method for analysing this type of data.