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Title: Spectral analysis of multivariate time series with applications to ocean waves Authors:  Adam Sykulski - Imperial College London (United Kingdom) [presenting]
Jake Grainger - Lancaster University (United Kingdom)
Philip Jonathan - Lancaster University / Shell Research Limited (United Kingdom)
Kevin Ewans - Met Ocean Research Limited (New Zealand)
Abstract: Ocean waves are monitored using buoys which measure three-dimensional displacement at high temporal frequencies over one hertz. Such multivariate measurements allow not only the frequency of waves to be measured, but also their direction, and how these evolve over time. Oceanographers jointly characterise this information in what is called the frequency-direction spectrum. We will discuss what this is and why it is important. Oceanographers have developed numerous parametric models for the frequency-direction spectrum, which can then be fitted to observations by approximating the empirical frequency-direction spectrum; however, the reality is that existing methodologies do a very poor job of fitting these parameters. We will discuss a new approach we have developed to fix this problem. Specifically, we think about how the data is fundamentally collected - as a three-dimensional (orthogonal) multivariate time series. We, therefore, convert the frequency-direction parametric models into multivariate spectral models and then use quasi-likelihood approaches to fit the parameters directly to the Fourier transforms of the observed multivariate data. This yields vastly improved parameter estimates in terms of both reduced bias and variance, as we shall demonstrate with simulations and applications to real data.