  This paper proposes stochastic models for the analysis of ocean surface
trajectories obtained from freely-drifting satellite-tracked instruments. The
proposed time series models are used to summarise large multivariate datasets
and infer important physical parameters of inertial oscillations and other
ocean processes. Nonstationary time series methods are employed to account for
the spatiotemporal variability of each trajectory. Because the datasets are
large, we construct computationally efficient methods through the use of
frequency-domain modelling and estimation, with the data expressed as
complex-valued time series. We detail how practical issues related to sampling
and model misspecification may be addressed using semi-parametric techniques
for time series, and we demonstrate the effectiveness of our stochastic models
through application to both real-world data and to numerical model output.
