Application of Kolmogorov complexity and universal codes to identity testing and nonparametric testing of serial independence for time series

TL;DR

This paper demonstrates how Kolmogorov complexity and universal coding can be used for hypothesis testing, specifically for identity and serial independence in time series, bridging information theory and statistical testing.

Contribution

It introduces novel methods leveraging Kolmogorov complexity and universal codes for identity and serial independence testing in time series analysis.

Findings

Proposes new hypothesis testing methods based on Kolmogorov complexity.

Shows applicability of universal codes for nonparametric serial independence testing.

Bridges information theory with classical statistical hypothesis testing.

Abstract

We show that Kolmogorov complexity and such its estimators as universal codes (or data compression methods) can be applied for hypotheses testing in a framework of classical mathematical statistics. The methods for identity testing and nonparametric testing of serial independence for time series are suggested.