Statistical analysis of coupled time series with Kernel Cross-Spectral Density operators

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Kernel Mean Embedding of Distributions: A Review and Beyonds (2016, methodology): “, financial data and brain activity data—were recently proposed in a series of works including Besserve et al. (2013), Chwialkowski and Gretton (2014), Chwialkowski et al. (2014). If one is interested in a serial dependency within a single time series, the test reduces to the i.i.d. case under null ”
A Wild Bootstrap for Degenerate Kernel Tests (2014, methodology): “Statistical tests based on distribution embeddings into reproducing kernel Hilbert spaces have been applied in many contexts, including two sample testing [19, 15, 31], tests of independence [17, 32, 4], tests of conditional independence [14, 32], and tests for higher order (Lancaster) interactions ”
A Kernel Independence Test for Random Processes (2014, methodology): “We then show that the normalized V -statistic associated with the function s has the same asymptotic distribution as the n · V (h, Z) distribution.”
Gaussian Processes for Independence Tests with Non-iid Data in Causal Inference (2015, background): “In Section 4.1, we state precise conditions under which our test is valid.”