Universal Codes as a Basis for Nonparametric Testing of Serial Independence for Time Series

TL;DR

This paper introduces new nonparametric tests for serial independence in time series using universal codes, applicable to stationary ergodic sources, with the ability to distinguish Markovian and independent sources.

Contribution

The paper proposes novel tests based on universal codes and predictors for assessing serial independence in time series, extending nonparametric testing methods.

Findings

Tests effectively distinguish Markovian from non-Markovian sources.

Applicable to finite alphabet stationary ergodic sources.

Provides a universal approach for independence testing.

Abstract

We consider a stationary and ergodic source $p$ generated symbols $x_1 ... x_t$ from some finite set $A$ and a null hypothesis $H_0$ that $p$ is Markovian source with memory (or connectivity) not larger than $m, (m >= 0).$ The alternative hypothesis $H_1$ is that the sequence is generated by a stationary and ergodic source, which differs from the source under $H_0$. In particular, if $m= 0$ we have the null hypothesis $H_0$ that the sequence is generated by Bernoully source (or the hypothesis that $x_1 ...x_t$ are independent.) Some new tests which are based on universal codes and universal predictors, are suggested.