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

Buoy data in the form of multivariate time series are routinely recorded at many locations in the world's oceans. Such data can help characterise the ocean wavefield by modelling the frequency-direction spectrum. State-of-the-art methods for estimating the parameters of such models do not make use of the full spatiotemporal content of the buoy observations due to unnecessary assumptions and smoothing. We explain how the multivariate debiased Whittle likelihood can be used to jointly estimate all parameters of such frequency-direction spectra directly from recorded time series. We apply the method to North Sea buoy data and discuss challenging practical issues.