A Kernel Independence Test for Random Processes

TL;DR

This paper introduces a nonparametric independence test for random processes using the Hilbert Schmidt Independence Criterion (HSIC), with new asymptotic analysis and a consistent p-value estimation method, outperforming bootstrap procedures especially on real-world data.

Contribution

It extends HSIC to random processes, providing asymptotic behavior analysis and a new p-value estimation method that improves independence testing accuracy.

Findings

The new test detects dependencies missed by linear methods.

Bootstrap procedures fail for random processes, leading to false positives.

The proposed method performs well on both artificial and real-world Forex data.

Abstract

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 .