椭圆型Ornstein-Uhlenbeck过程
The Elliptical Ornstein-Uhlenbeck Process
摘要：
我们介绍椭圆Ornstein-Uhlenbeck（椭圆）过程，这是一个众所周知的单变量椭圆过程的推广到二元时间序列。这一过程在复平面上映射出随时间的椭圆随机振荡，这在耦合双变量时间序列的许多应用中都可以观察到。该模型的吸引力在于，椭圆振荡是使用一个简单的一阶随机微分方程（NMD）产生的，而替代模型需要更复杂的矢量化或更高阶的NMD表示。第二个有用的特征是，参数估计可以在频域中使用惠特尔李克图半参数地执行。我们确定的模型，包括平稳性的条件，和椭圆振荡的几何结构的属性。我们证明了该模型的实用性，通过测量地球的极地运动的周期性和椭圆特性。
英文摘要：
We introduce the elliptical Ornstein-Uhlenbeck (OU) process, 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 stochastic differential equation (SDE), whereas alternative models require more complicated vectorised or higher order SDE representations. The second useful feature is that parameter estimation can be performed semi-parametrically in the frequency domain using the Whittle Likelihood. We determine 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.
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