  Modeling the trajectories of animals is challenging due to the complexity of
their behaviors, the influence of unpredictable environmental factors,
individual variability, and the lack of detailed data on their movements.
Additionally, factors such as migration, hunting, reproduction, and social
interactions add additional layers of complexity when attempting to accurately
forecast their movements. In the literature, various models exits that aim to
study animal telemetry, by modeling the velocity of the telemetry, the
telemetry itself or both processes jointly through a Markovian process. In this
work, we propose to model the velocity of each coordinate axis for animal
telemetry data as a fractional Ornstein-Uhlenbeck (fOU) process. Then, the
integral fOU process models position data in animal telemetry. Compared to
traditional methods, the proposed model is flexible in modeling long-range
memory. The Hurst parameter $H \in (0,1)$ is a crucial parameter in integral
fOU process, as it determines the degree of dependence or long-range memory.
The integral fOU process is nonstationary process. In addition, a higher Hurst
parameter ($H > 0.5$) indicates a stronger memory, leading to trajectories with
transient trends, while a lower Hurst parameter ($H < 0.5$) implies a weaker
memory, resulting in trajectories with recurring trends. When H = 0.5, the
process reduces to a standard integral Ornstein-Uhlenbeck process. We develop a
fast simulation algorithm of telemetry trajectories using an approach via
finite-dimensional distributions. We also develop a maximum likelihood method
for parameter estimation and its performance is examined by simulation studies.
Finally, we present a telemetry application of Fin Whales that disperse over
the Gulf of Mexico.
