A Kernel Independence Test for Random Processes
This work addresses the need for reliable non-parametric independence tests in time-series and sequential data analysis, offering a novel solution for domains like finance, but it is incremental as it builds on existing HSIC methods.
The authors tackled the problem of testing independence between two random processes by extending the Hilbert-Schmidt Independence Criterion (HSIC) from i.i.d. data to random processes, establishing its asymptotic behavior and proposing a consistent p-value estimation method that outperforms earlier bootstrap procedures, as shown in tests on artificial and Forex data where it discovered dependencies missed by linear approaches and reduced false positives.
A new non parametric approach to the problem of testing the independence of two random process is developed. The test statistic is the Hilbert Schmidt Independence Criterion (HSIC), which was used previously in testing independence for i.i.d pairs of variables. The asymptotic behaviour of HSIC is established when computed from samples drawn from random processes. It is shown that earlier bootstrap procedures which worked in the i.i.d. case will fail for random processes, and an alternative consistent estimate of the p-values is proposed. Tests on artificial data and real-world Forex data indicate that the new test procedure discovers dependence which is missed by linear approaches, while the earlier bootstrap procedure returns an elevated number of false positives. The code is available online: https://github.com/kacperChwialkowski/HSIC .