Universal Codes as a Basis for Time Series Testing

TL;DR

This paper introduces a universal data compression-based approach for hypothesis testing in stationary ergodic processes, enabling nonparametric tests for various properties without prior distribution knowledge.

Contribution

It proposes a novel universal coding-based framework for hypothesis testing applicable to multiple problems in time series analysis, even with unknown codeword length distributions.

Findings

Applicable with standard archivers for practical testing

Enables nonparametric tests for goodness-of-fit, independence, and homogeneity

Works without prior knowledge of distribution laws

Abstract

We suggest a new approach to hypothesis testing for ergodic and stationary processes. In contrast to standard methods, the suggested approach gives a possibility to make tests, based on any lossless data compression method even if the distribution law of the codeword lengths is not known. We apply this approach to the following four problems: goodness-of-fit testing (or identity testing), testing for independence, testing of serial independence and homogeneity testing and suggest nonparametric statistical tests for these problems. It is important to note that practically used so-called archivers can be used for suggested testing.