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Ocean buoy data in the form of high frequency multivariate time series areroutinely recorded at many locations in the world's oceans. Such data can beused to characterise the ocean wavefield, which is important for numeroussocio-economic and scientific reasons. This characterisation is typicallyachieved by modelling the frequency-direction spectrum, which decomposesspatiotemporal variability by both frequency and direction. State-of-the-artmethods for estimating the parameters of such models do not make use of thefull spatiotemporal content of the buoy observations due to unnecessaryassumptions and smoothing steps. We explain how the multivariate debiasedWhittle likelihood can be used to jointly estimate all parameters of suchfrequency-direction spectra directly from the recorded time series. Whenapplied to North Sea buoy data, debiased Whittle likelihood inference revealssmooth evolution of spectral parameters over time. We discuss challengingpractical issues including model misspecification, and provide guidelines forfuture application of the method.

A multivariate pseudo-likelihood approach to estimating directional ocean wave models