ae5e3ce40e0404a45ecacaaf05e5f735-Reviews.html

We are grateful to the reviewers for their careful reading of our manuscript and their suggestions. KCSD is a complex object to study and an important aspect of our contribution is to estimate its properties with good asymptotic result under mild conditions. We introduce an unbiased estimate and a statistical test using fast algorithms which are easily applicable to many datasets. Our results cannot be found elsewhere and further work can build on our mathematical treatment to assess statistical properties of kernel methods for stationary data. Most importantly, this contribution aims at bringing results from kernel methods to communities that are in important need for general time series analysis techniques with good statistical properties. Measures describing the dependency structure of the data without model assumptions, such as the linear cross-spectrum, became standard in applications such as Neurophysiology.