Signal Processing Approach to Study Multifractality and Singularity of Solar Wind Speed Time Series

Authors: Tushnik Sarkar, Mofazzal H. Khondekar, Subrata Banerjee

Abstract:

This paper investigates the nature of the fluctuation of the daily average Solar wind speed time series collected over a period of 2492 days, from 1^st January, 1997 to 28^th October, 2003. The degree of self-similarity and scalability of the Solar Wind Speed signal has been explored to characterise the signal fluctuation. Multi-fractal Detrended Fluctuation Analysis (MFDFA) method has been implemented on the signal which is under investigation to perform this task. Furthermore, the singularity spectra of the signals have been also obtained to gauge the extent of the multifractality of the time series signal.

Keywords: Detrended fluctuation analysis, generalized Hurst exponent, holder exponents, multifractal exponent, multifractal spectrum, singularity spectrum, time series analysis.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1339884

References:

[1] F. Culot, "Participation in the Norwegian Dayside Auroral Observation Programme on Svalbard," University de Versailles Saint-Quentin-en-Yvelines, 2000, available online from http://culot.org/sources/rapportmaitrise.doc, Accessed on 10/06/2016.
[2] L. Telesca, V. Lapenna, and M. Macchiato, “Multifractal fluctuations in earthquake-related geoelectrical signals,” New J. Phys., 2005, vol. 7, pp. 214–228.
[3] R.G. Kavasseri, R. Nagarajan, "A multifractal description of wind speed records," Chaos, Solitons & Fractals, 2005, vol. 24, pp. 165-173.
[4] Z. Hong, D. Keqiang, “Multifractal Analysis of Traffic Flow Time Series,” Journal of Hebei University of Engineering, 2009, vol. 26, pp. 109-112.
[5] K. M. Hossain, D. N. Ghosh,and K. Ghosh, “Investigating multifractality of solar irradiance data through wavelet based multifractal spectral analysis”, Signal Process. Int. J. (SPIJ), 2009, vol. 3, No. 4, pp. 83-94.
[6] C. Barman, H. Chaudhuri, D. Ghose, A. Deb, and B. Sinha, “Multifractal Detrended Fluctuation Analysis of Seismic Induced Radon-222 Time Series, ”Journal of Earthquake Science and Engineering, 2014,Vol-1, PP 59-79.
[7] H. Feng, Y. Xu “Multifractal Detrended Fluctuation Analysis of WLAN Traffic, ”Wireless Personal Communications, 2012, Volume 66, pp 385–395.
[8] S. M. Ossadnik, S. V. Buldyrev, A. L. Goldberger, “Correlation approach to identify coding regions in DNA sequences”, Biophys.J,1994, vol. 67, pp. 64-70.
[9] S. Benbachir, M. H. Alaoui,” A Multifractal Detrended Fluctuation Analysis of the Moroccan Dirham with respect to the US Dollar,” 2011, vol.6, No.2, pp. 287-300.
[10] L. Erhui, M. Xingmin, Z. Guangju, and G. Peng,” Multifractal Detrended Fluctuation Analysis of Streamflow in the Yellow River Basin, China,” Water ,2015, vol.7, pp. 1670-1686.
[11] J. W. Kantelhardt, E. K. Bunde, H. H. Rego, S Havlin, and A. Bunde, “Detecting long range correlations with detrended fluctuation analysis”, Physica A, 2001, vol.295, No.3, pp. 441-454.
[12] K. M. Hossain, D. N. Ghosh, K. Ghosh, and A. K. Bhattacharya, “Multifractality and singularity of 8B solar neutrino flux signals from Sudbury Neutrino Observatory,”IET Signal Process., 2011, vol.5, No.7, pp. 690-700.
[13] J. W. Kantelhardt, S. A. Zschiegner, and E. K. Bunde, “Multifractal detrended fluctuation analysis on nonstationary time series, ”Physica A, 2002, vol.316, No.1-4, pp. 87-114.
[14] T. Sarkar, R. Ray, M. H. Khondekar, K. Ghosh, and S. Banerjee,” Chaos and periodicity in solar wind speed: cycle 23,” Astrophysics and Space Science, 2015, vol.357, No. 2, pp. 1-10.
[15] P. Oswiecimka, J. Kwapien, and S. Drozdz, “Wavelet versus detrendedfluctuation analysis of multifractal structures, ”Phys. Rev. E, 2005, vol.74, No.1, pp. 1-17.
[16] T. James, S. Eubank, A. Longtin, et al., “Testing for nonlinearity in time series: the method of surrogate data, ”Physica D: Nonl. Phen., 1992, vol. 58, No.1–4, pp. 77–94.