Long-range time dependence in the cross-correlation function

Detection of a long-range time dependence in the radial cross-correlation f unction is normally difficult because of the oscillatory behavior of the cr oss-correlation tail, its low level of coherence, and noise contamination. This problem persists, even with large statistical samples. In this paper, a method for investigating long-range dependence in a single time series is extended to the calculation of the cross-correlation function. With this m ethod and for time series with long-range time correlations, the accuracy o f the determination of the cross-correlation function for long time lags is improved. The method is tested by applying it to fractional Gaussian noise and to the fluxes in a running sandpile model. This analysis technique can be applied to the detection of avalanche-type transport in magnetic confin ement devices. (C) 1999 American Institute of Physics. [S1070-664X(99)02402 -7].