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The elliptical Ornstein–Uhlenbeck process
Statistics and Its Interface ( IF 0.8 ) Pub Date : 2022-07-27 , DOI: 10.4310/21-sii714
Adam Sykulski, Sofia Olhede, Hanna Sykulska-Lawrence

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.

中文翻译:

椭圆 Ornstein-Uhlenbeck 过程

我们介绍了椭圆 Ornstein-Uhlenbeck (OU) 过程,它是将著名的单变量 OU 过程推广到双变量时间序列。这个过程映射出复杂平面中随时间推移的椭圆随机振荡,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 (SDE) 生成的,而替代模型需要更复杂的矢量化或更高阶 SDE 表示。第二个有用的特性是可以使用 Whittle 似然在频域中半参数地执行参数估计。我们确定模型的属性,包括平稳性条件和椭圆振荡的几何结构。
更新日期:2022-07-28
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