The goal of this paper is to develop a measure for characterizing complex dependence between time series that cannot be captured by traditional measures such as correlation and coherence. Our approach is to use copula models of functionals of the Fourier coefficients which is a generalization of coherence. Here, we use standard parametric copula models with a single parameter from both elliptical and Archimedean families. Our approach is to analyze changes in activity in local field potentials in the rat cortex prior to and immediately following the onset of stroke. We present the necessary theoretical background, the multivariate models and an illustration of our methodology on these local field potential data. Simulations with nonlinear dependent data reveal that there is information that is missed by not taking into account dependence on specific frequencies. Moreover, these simulations demonstrate how our proposed method captures more complex nonlinear dependence between time series. Finally, we illustrate our copula-based approach in the analysis of local field potentials of rats.

本文的目的是开发一种方法，以表征时间序列之间的复杂依赖性，而相关性和相干性等传统方法无法捕获这些时间序列之间的复杂依赖性。我们的方法是使用傅里叶系数泛函的copula模型，这是相干性的概括。在这里，我们使用来自椭圆族和阿基米德族的带有单个参数的标准参数系对模型。我们的方法是在中风发作之前和之后分析大鼠皮层局部场电位活动的变化。我们介绍了必要的理论背景，多元模型以及这些局部领域潜力数据的方法论说明。用非线性相关数据进行的仿真表明，由于没有考虑对特定频率的依赖性，因此会丢失某些信息。此外，这些仿真证明了我们提出的方法如何捕获时间序列之间更复杂的非线性相关性。最后，我们举例说明了我们基于copula的方法，用于分析大鼠的局部场电势。