Testing power-law cross-correlations: Rescaled covariance test

TL;DR

This paper introduces a new statistical test, the rescaled covariance test, to detect power-law cross-correlations in time series data, especially useful in financial market analysis.

Contribution

The paper presents a novel test based on covariance divergence of partial sums, improving detection of long-range cross-correlations with robust statistical properties.

Findings

The test effectively distinguishes short- and long-range cross-correlations.

Application to financial data shows power-law cross-correlations between volatility, volume, and returns.

The method provides a starting point for analyzing long-range dependencies in time series.

Abstract

We introduce a new test for detection of power-law cross-correlations among a pair of time series - the rescaled covariance test. The test is based on a power-law divergence of the covariance of the partial sums of the long-range cross-correlated processes. Utilizing a heteroskedasticity and auto-correlation robust estimator of the long-term covariance, we develop a test with desirable statistical properties which is well able to distinguish between short- and long-range cross-correlations. Such test should be used as a starting point in the analysis of long-range cross-correlations prior to an estimation of bivariate long-term memory parameters. As an application, we show that the relationship between volatility and traded volume, and volatility and returns in the financial markets can be labeled as the one with power-law cross-correlations.