Eur. Phys. J. B (2013) 86: 418
https://doi.org/10.1140/epjb/e2013-40705-y

Regular Article

Testing power-law cross-correlations: rescaled covariance test

¹ Institute of Information Theory and Automation, Academy of Sciences of the Czech Republic, Pod Vodarenskou Vezi 4, 182 08 Prague, Czech Republic
² Institute of Economic Studies, Faculty of Social Sciences, Charles University in Prague, Opletalova 26, 110 00 Prague, Czech Republic

^a e-mail: kristouf@utia.cas.cz

Received: 24 July 2013
Received in final form: 26 August 2013
Published online: 7 October 2013

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 power-law cross-correlated one.