Abstract

Many applications require the analysis of complex interactions between time series. These interactions can be non-linear and involve vector valued as well as complex data structures such as graphs or strings. Here we provide a general framework for the statistical analysis of these dependencies when random variables are sampled from stationary time-series of arbitrary objects. To achieve this goal, we study the properties of the Kernel Cross-Spectral Density (KCSD) operator induced by positive definite kernels on arbitrary input domains. This framework enables us to develop an independence test between time series, as well as a similarity measure to compare different types of coupling. The performance of our test is compared to the HSIC test using i.i.d. assumptions, showing improvements in terms of detection errors, as well as the suitability of this approach for testing dependency in complex dynamical systems. This similarity measure enables us to identify different types of interactions in electrophysiological neural time series.