Reliable scaling exponent estimation of long-range correlated noise in the presence of random spikes

Detrended fluctuation analysis (DFA) has been used widely to determine possible long-range correlations in data obtained from diverse settings. In a recent study [Z. Chen, P.Ch. Ivanov, K. Hu, H.E. Stanley, Effects of nonstationarities on detrended fluctuation analysis, Phys Rev E 65 (2002) 041107], uncorrelated random spikes superimposed on the long-range correlated noise (LR noise) were found to affect DFA scaling exponent estimates. In this brief communication, singular-value decomposition (SVD) filter is proposed to minimize the effect random spikes superimposed on LR noise, thus facilitating reliable estimation of the scaling exponents. The effectiveness of the proposed approach is demonstrated on random spikes sampled from normal and uniform distributions.