On detecting the dependence of time series

TL;DR

This paper proposes a heuristic method to detect weak dependence in time series by comparing sample characteristic functionals with those of a benchmark series, demonstrated on financial data.

Contribution

It introduces a novel heuristic approach for identifying dependence in time series where traditional methods fail, especially in weak dependence scenarios.

Findings

Method effectively detects weak dependence in financial time series

Comparison with benchmark series reveals correlation levels

Experimental results support the method's practical utility

Abstract

This short note suggests a heuristic method for detecting the dependence of random time series that can be used in the case when this dependence is relatively weak and such that the traditional methods are not effective. The method requires to compare some special functionals on the sample characteristic functions with the same functionals computed for the benchmark time series with a known degree of correlation. Some experiments for financial time series are presented.