Eur. Phys. J. B 56, 47-52 (2007)
https://doi.org/10.1140/epjb/e2007-00089-3

Power-law autocorrelated stochastic processes with long-range cross-correlations

¹ Faculty of Civil Engineering, University of Rijeka, 51000 Rijeka, Croatia
² Zagreb School of Economics and Management, 10000 Zagreb, Croatia
³ Center for Polymer Studies and Department of Physics, Boston University, Boston, MA, 02215, USA
⁴ Institute of Solid State Physics, Bulgarian Academy of Sciences, 1784 Sofia, Bulgaria

Corresponding authors: ^a dffu@bu.edu - ^b plamen@buphy.bu.edu

Received: 17 July 2006
Revised: 16 January 2007
Published online: 4 April 2007

Abstract

We develop a stochastic process with two coupled variables where the absolute values of each variable exhibit long-range power-law autocorrelations and are also long-range cross-correlated. We investigate how the scaling exponents characterizing power-law autocorrelation and long-range cross-correlation behavior in the absolute values of the generated variables depend on the two parameters in our model. In particular, if the autocorrelation is stronger, the cross-correlation is also stronger. We test the utility of our approach by comparing the autocorrelation and cross-correlation properties of the time series generated by our model with data on daily returns over ten years for two major financial indices, the Dow Jones and the S&P500, and on daily returns of two well-known company stocks, IBM and Microsoft, over five years.