  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.

Statistical Finance