  Ocean buoy data in the form of high frequency multivariate time series are
routinely recorded at many locations in the world's oceans. Such data can be
used to characterise the ocean wavefield, which is important for numerous
socio-economic and scientific reasons. This characterisation is typically
achieved by modelling the frequency-direction spectrum, which decomposes
spatiotemporal variability by both frequency and direction. 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 steps. We explain how the multivariate debiased
Whittle likelihood can be used to jointly estimate all parameters of such
frequency-direction spectra directly from the recorded time series. When
applied to North Sea buoy data, debiased Whittle likelihood inference reveals
smooth evolution of spectral parameters over time. We discuss challenging
practical issues including model misspecification, and provide guidelines for
future application of the method.
