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Minimizing the effect of periodic and quasi-periodic trends in detrended fluctuation analysis. (English) Zbl 1093.62506
Summary: Detrended fluctuation analysis (DFA) has been proposed as a robust technique to determine possible long-range correlations in power-law processes. However, recent studies have reported the susceptibility of DFA to periodic trends, which can result in spurious crossovers. In this brief report, we propose a technique based on singular value decomposition to minimize the effect of both periodic as well as quasi-periodic trends in DFA estimation. The effectiveness of the proposed technique is demonstrated on publicly available data sets.

MSC:
62-99Statistics (MSC2000)
Software:
longmemo
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References:
[1] Peng, C. -K.; Buldyrev, S. V.; Havlin, S.; Simons, M.; Stanley, H. E.; Goldberger, A. L.: Mosaic organization of DNA nucleotides. Phys. rev. E 49, 1685-1689 (1994)
[2] Hu, K.; Ivanov, P. Ch.; Chen, Z.; Carpena, P.; Eugene, S. H.: Effect of trends on detrended fluctuation analysis. Phys. rev. E 64, 011114-011133 (2001)
[3] Bassingthwaighte, J. B.; Liebovitch, L. S.; West, B. J.: Fractal physiology. (1995)
[4] Levy, V. J.; Reidi, R. H.: Fractional Brownian motion and data traffic modeling: the other end of the spectrum. Fractals in engineering (1996)
[5] Gopikrishnan, P.; Plerou, V.; Gabaix, X.; Stanley, H. E.: Statistical properties of share volume traded in financial markets. Phys rev E stat phys plasmas fluids relat interdiscip topics 62, R4493-R4496 (2000)
[6] Stanely, H. E.; Amaral, L. A. N.; Goldberger, A. L.; Havlin, S.; Ivanov, P. Ch.; Peng, C. -K.: Statistical physics and physiologymonofractal and multifractal approaches. Physica A 270, 309-324 (1999)
[7] Ivanov, P. Ch.; Amaral, L. A. N.; Goldberger, A. L.; Havlin, S.; Rosenblum, M. G.; Struzik, Z. R.; Stanley, H. E.: Multifractality in human heartbeat dynamics. Nature 399, 461-465 (1999)
[8] Kantelhardt, J. W.; Zschiegner, S. A.; Koscielny-Bunde, E.; Havlin, S.; Bunde, A.; Eugene, S. H.: Multifractal detrended fluctuation analysis of nonstationary time series. Physica A 316, 87 (2002) · Zbl 1001.62029
[9] Beran, J.: Statistics for long-memory processes. (1994) · Zbl 0869.60045
[10] Peng, C. -K.; Havlin, S.; Eugene, S. H.; Goldberger, A. L.: Quantification of scaling exponents and crossover phenomena in nonstationary heartbeat time series. Chaos 5, 82-87 (1995)
[11] Mills, T. C.: Modeling trends and cycles in economic time series. (2003)
[12] Golub, G.; Van Loan, C.: Matrix computations. (1996) · Zbl 0865.65009
[13] Proakis, J. G.; Manolakis, D. G.: Digital signal processingprinciples algorithms and applications. (1995)
[14] Pisarenko, V. F.: The retrieval of harmonics from a covariance function. Geophys. J. Roy. astron. Soc. 33, 347-366 (1973) · Zbl 0287.62048
[15] Caratheodory, C.; Fejer, L.: Uber den zussamenghang der extemen von harmonischen funktionen mit ihren koeffizienten und uber den Picard-landauschen satz. Rend. circolo mat. Palermo 32, 218-239 (1911)
[16] Sidiropoulos, N. D.: Generalizing Carathéodory’s uniqueness of harmonic parameterization to N dimensions. IEEE trans. Inform. theory 47, 1687-1690 (2001) · Zbl 1003.94012
[17] R. Nagarajan, Local analysis of dissipative dynamical systems, Int. J. Bifurcation Chaos 15 (5) (2005), in press. · Zbl 1092.37527
[18] Ashkenazy, Y.; Ivanov, P. Ch.; Havlin, S.; Peng, C. -K.; Goldberger, A. L.; Stanley, H. E.: Magnitude and sign correlations in heartbeat fluctuations. Phy. rev. Lett. 86, No. 9, 1900-1903 (2001)
[19] Kantelhardt, J. W.; Koscielny-Bunde, E.; Rego, H. A.; Havlin, S.; Bunde, A.: Detecting long-range correlations with detrended fluctuation analysis. Physica A 295, 441 (2001) · Zbl 0978.37057
[20] Chen, Z.; Ivanov, P. Ch.; Hu, K.; Stanley, H. E.: Effects of nonstationarities on detrended fluctuation analysis. Phys. rev. E 65, 041107 (2002)