Smoothed detrended fluctuation analysis. (English) Zbl 07184804
Summary: The method of detrended fluctuation analysis (DFA) is useful in revealing the extent of long-range dependence, it has successfully been applied to different fields of interest. In this paper we proposed a smoothed detrended fluctuation analysis method based on the principle of wavelet shrinkage. The procedure is illustrated and compared with the DFA method by Monte Carlo simulations on fractional Gaussian noise models.
MSC:
| 62G05 | Nonparametric estimation |
| 62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |
Keywords:
long-range dependence; detrended fluctuation analysis; fractional Gaussian noise; Hurst exponent; wavelet shrinkageReferences:
| [1] | Beran J. Statistics for long memory processes. New York: Chapman & Hall; 1994. [Google Scholar] · Zbl 0869.60045 |
| [2] | Hurst HR. Long-term storage in reservoirs. Trans Am Soc Civil Eng. 1951;116:770-799. [Google Scholar] |
| [3] | Peng C, Buldyrev SV, Havlin S, Simons M, Stanley HE, Goldberger AL. Mosaic organization of DNA nucleotides. Phys Rev E. 1994;49(5):1685-1689. doi: 10.1103/PhysRevE.49.1685[Crossref], [PubMed], [Web of Science ®], [Google Scholar] |
| [4] | Grech D, Mazur Z. Can one make any crash prediction in finance using the local Hurst exponent idea?. Phys A. 2004;336:133-145. doi: 10.1016/j.physa.2004.01.018[Crossref], [Web of Science ®], [Google Scholar] |
| [5] | Grech D, Pamula G. The local Hurst exponent of the financial time series in the vicinity of crashes on the Polish stock exchange market. Phys A. 2008;387:4299-4308. doi: 10.1016/j.physa.2008.02.007[Crossref], [Web of Science ®], [Google Scholar] |
| [6] | Grech D. Global and local approaches describing critical phenomena on the developing and developed financial markets. In: Takayasu M, Watanabe T, Takayasu H, editors. Econophysics approaches to large-scale business data and financial crisis. Tokyo: Springer; 2010. p. 149-172. [Crossref], [Google Scholar] |
| [7] | Yeh R-G, Shieh J-S, Han Y-Y, Wang Y-J, Tseng S-C. Detrended fluctuation analyses of short-term heart rate variability in surgical intensive care units. Biomed Eng-Appl Basis Commun. 2006;18:67-72. doi: 10.4015/S1016237206000130[Crossref], [Google Scholar] |
| [8] | Koscielny-Bunde E, Roman HE, Bunde A, Havlin S, Schellnhuber H-J. Long-range power-law correlations in local daily temperature fluctuations. Phil Mag B. 1998;77:1331-1340. doi: 10.1080/13642819808205026[Taylor & Francis Online], [Web of Science ®], [Google Scholar] |
| [9] | Bola M, Gall C, Sabel BA. Disturbed temporal dynamics of brain synchronization in vision loss. Cortex. 2015;67:134-146. doi: 10.1016/j.cortex.2015.03.020[Crossref], [PubMed], [Web of Science ®], [Google Scholar] |
| [10] | Choi J-S, Kang D-W, Seo J-W, Tack G-R. Reliability of the walking speed and gait dynamics variables while walking on a feedback-controlled treadmill. J Biomech. 2015;48(7):1336-1339. doi: 10.1016/j.jbiomech.2015.02.047[Crossref], [PubMed], [Web of Science ®], [Google Scholar] |
| [11] | Crato N, Linhares RR, Lopes SRC. Statistical properties of detrended fluctuation analysis. J Statist Comput Simul. 2010;80(6):625-641. doi: 10.1080/00949650902755152[Taylor & Francis Online], [Web of Science ®], [Google Scholar] · Zbl 1432.62295 |
| [12] | Esen H, Ata N, Esen F. Transitions in skin blood flow fractal scaling: the importance of fluctuation amplitude in microcirculation. Microvascular Res. 2015;97:6-12. doi: 10.1016/j.mvr.2014.07.014[Crossref], [PubMed], [Web of Science ®], [Google Scholar] |
| [13] | Rhea CK, Kiefer AW, Wright WG, Raisbeck LD, Haran FJ. Interpretation of postural control may change due to data processing techniques. Gait Posture. 2015;41(2):731-735. doi: 10.1016/j.gaitpost.2015.01.008[Crossref], [PubMed], [Web of Science ®], [Google Scholar] |
| [14] | Setty VA, Sharma AS. Characterizing detrended fluctuation analysis of multifractional Brownian motion. Phys A: Statist Mech Appl. 2015;419:698-706. doi: 10.1016/j.physa.2014.10.016[Crossref], [Web of Science ®], [Google Scholar] |
| [15] | Taqqu MS, Teverovsky V, Willinger W. Estimators for long-range dependence: an empirical study. Fractals. 1995;3(4):785-798. doi: 10.1142/S0218348X95000692[Crossref], [Web of Science ®], [Google Scholar] · Zbl 0864.62061 |
| [16] | Bardet J-M, Kammoun I. Asymptotic properties of the detrended fluctuation analysis of long-range dependence processes. IEEE Trans Inf Theory. 2008;54(5):2041-2052. doi: 10.1109/TIT.2008.920328[Crossref], [Web of Science ®], [Google Scholar] · Zbl 1328.60098 |
| [17] | Donoho DL, Johnstone JM. Ideal spatial adaptation by wavelet shrinkage. Biometrika. 1994;81:425-455. doi: 10.1093/biomet/81.3.425[Crossref], [Web of Science ®], [Google Scholar] · Zbl 0815.62019 |
| [18] | Donoho DL, Johnstone IM, Kerkyacharian G, Picard D. Wavelet shrinkage: asymptopia? J R Statist Soc. 1995;57:301-369. [Google Scholar] · Zbl 0827.62035 |
| [19] | Ogden RT. Essential wavelets for statistical applications and data analysis. Cambridge: Birkhäuser; 1997. [Crossref], [Google Scholar] · Zbl 0868.62033 |
| [20] | Vidakovic B. Statistical modeling by wavelets. New York: Wiley; 1999. [Crossref], [Google Scholar] · Zbl 0924.62032 |
| [21] | Meyer Y. Wavelets: algorithms and applications. Philadelphia: SIAM; 1993. [Google Scholar] · Zbl 0821.42018 |
| [22] | Donoho DL, Johnstone IM. Adapting to unknown smoothness via wavelet shrinkage. J Amer Statist Assoc. 1995;90:1200-1224. doi: 10.1080/01621459.1995.10476626[Taylor & Francis Online], [Web of Science ®], [Google Scholar] · Zbl 0869.62024 |
| [23] | Hu K, Ivanov PC, Chen Z, Carpena P, Stanley HE. Effect of trends on detrended fluctuation analysis. Phys Rev E. 2001;64:011114. [Crossref], [Web of Science ®], [Google Scholar] |
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