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
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.
Key words: Statistical and Nonlinear Physics
© EDP Sciences, Società Italiana di Fisica and Springer-Verlag, 2013