The elliptical Ornstein–Uhlenbeck process

We introduce the elliptical Ornstein-Uhlenbeck (OU) process, which is a generalisation of well-known univariate OU process to bivariate time series. This maps out stochastic oscillations over in complex plane, are observed many applications coupled The appeal model that generated using one simple first order SDE, whereas alternative models require more complicated vectorised or higher SDE representations. second useful feature parameter estimation can be performed robustly frequency domain only modelled and power spectral density, without having compute cross spectra individual series components. determine properties including conditions for stationarity, geometrical structure oscillations. demonstrate utility by measuring periodic Earth's polar motion.