论文标题
椭圆形的Ornstein-Uhlenbeck过程
The Elliptical Ornstein-Uhlenbeck Process
论文作者
论文摘要
我们介绍了椭圆形的Ornstein-Uhlenbeck（OU）过程，这是对双变量时间序列的众所周知的单变量OU过程的概括。该过程在复杂平面中绘制了椭圆形的随机振荡，这在耦合双变量时间序列的许多应用中都可以观察到。该模型的吸引力是使用一个简单的一阶随机微分方程（SDE）生成椭圆振荡，而替代模型则需要更复杂的矢量化或更高阶SDE表示。第二个有用的功能是，可以使用惠特可能性在频域中在频域中进行半参数进行参数估计。我们确定模型的性质，包括平稳性的条件以及椭圆振荡的几何结构。我们通过测量地球极性运动的周期性和椭圆性特性来证明该模型的实用性。
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.
