Multidimensional Integral Fractional Ornstein–Uhlenbeck Process With an Application to Animal Movement

Fractional Ornstein–Uhlenbeck (fOU) processes model temporal dependence and memory, including long‐range dependence, while retaining the classical Ornstein–Uhlenbeck process as a special case. We extend the integral fractional Ornstein–Uhlenbeck (ifOU) process to a multidimensional setting for animal telemetry. Longitude, Latitude, and Altitude velocities are represented by coordinate‐specific fOU processes driven by a multivariate fractional Brownian motion, allowing each coordinate to retain its own damping, scale, and Hurst parameters. We establish covariance validity, characterize the admissible cross‐correlation region, and derive the asymptotic behavior of cross‐covariances and separated increments. We develop procedures for finite‐dimensional simulation, Gaussian likelihood inference, and conditional velocity reconstruction. Replicated simulations examine the estimation of cross‐coordinate correlations, while joint estimation of the complete parameter vector is illustrated for one three‐dimensional trajectory. The proposed model is applied to telemetry records from five common noctule bats migrating in Germany, including three trajectories with Altitude measurements.