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Title: The elliptical Ornstein-Uhlenbeck process Authors:  Adam Sykulski - Lancaster University (United Kingdom) [presenting]
Sofia Olhede - EPFL (Switzerland)
Abstract: The elliptical Ornstein-Uhlenbeck (OU) process is introduced, which is a generalisation of the well-known univariate OU process to bivariate time series. This process maps out elliptical stochastic oscillations over time in the complex plane, which are observed in many applications of coupled bivariate time series. The appeal of the model is that elliptical oscillations are generated using one simple first-order SDE, whereas alternative models require more complicated vectorised or higher-order SDE representations. The second useful feature is that parameter estimation can be performed robustly and quickly in the frequency domain using FFTs of complex-valued data. We determine some properties of the model including the conditions for stationarity, and the geometrical structure of the elliptical oscillations. We demonstrate the utility of the model by measuring periodic and elliptical properties of Earth's polar motion including the Chandler wobble.