Detrended cross-correlation analysis for non-stationary time series with periodic trends

¹ Department of Physics, Faculty of Natural Sciences, University of Zagreb - 10000 Zagreb, Croatia
² Center for Polymer Studies and Department of Physics, Boston University - Boston, MA 02215, USA
³ Department of Physics, Faculty of Civil Engineering, University of Rijeka - 51000 Rijeka, Croatia
⁴ Zagreb School of Economics and Management - 10000 Zagreb, Croatia

^a davorh@phy.hr

Received: 27 January 2011
Accepted: 7 March 2011

Abstract

Noisy signals in many real-world systems display long-range autocorrelations and long-range cross-correlations. Due to periodic trends, these correlations are difficult to quantify. We demonstrate that one can accurately quantify power-law cross-correlations between different simultaneously recorded time series in the presence of highly non-stationary sinusoidal and polynomial overlying trends by using the new technique of detrended cross-correlation analysis with varying order ℓ of the polynomial. To demonstrate the utility of this new method —which we call DCCA-ℓ(n), where n denotes the scale— we apply it to meteorological data.