Multifractal spectrum distribution based on detrending moving average |
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| Institution: | 1. School of Optical Electrical and Computer Engineering, University of Shanghai for Science and technology, Shanghai 200093, China;2. School of Electronic and Optical Engineering, Nanjing University of Science and technology, Nanjing 210094, China;1. Academy of Mathematics and Statistics, Hubei engineering University, China;2. Academy of Mathematics and Systems Science, University of Chinese Academy of Sciences, China;3. School of Statistics, Capital University of Economics and Finance, China;4. School of Mathematics and Statistics, University of Science and Technology of China, China;1. Department of Physics, Jadavpur University, Kolkata 700032, India;2. Department of Physics, Behala College, Parnasree Pally, Kolkata 700060, India;3. Department of Electrical Engineering, Dr. Sudhir Chandra Sur Degree Engineering College, Dum Dum, Kolkata 700074, India;1. Institute of Earthquake Prediction Theory and Mathematical Geophysics, Russian Academy of Sciences, Profsoyuznaya 84/32, Moscow 117997, Russia;2. Institute of Marine Geology and Geophysics, FEB RAS, ul. Nauki, 1B, Yuzhno-Sakhalinsk 693022, Russia;1. Physics Department, North Bengal University, Siliguri 734013, India;2. Computer and Information Sciences Department, SUNY, Fredonia, NY 14063, United States |
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| Abstract: | The time-singularity multifractal spectrum distribution (MFSD) has been proposed recently as a generalized singularity spectrum in a time varying framework. In this paper, we aim at putting forward a new algorithm i.e. MFSD based on detrending moving average (DMA-MFSD) to determine MFSD, which is also a generalization of multifractal detrending moving average (MF-DMA) method. We relate DMA-MFSD method to the MFSD based on the standard partition function, and prove that both approaches are equivalent for fractal time series with compact support. The performance of the DMA-MFSD methods with different moving windows is studied using synthetic fractional Gaussian noise (fGn), binomial multiplicative cascades (BMC) with analytical solutions and real sea clutter data. We find that the estimated DMA-MFSD is in good accordance with the detrended fluctuation analysis based multifractal spectrum distribution (DFA-MFSD) and the theoretical analysis. Overall, the backward DMA-MFSD method has the best performance, which provides the most accurate estimates of the time-singularity MFSD, while the centered DMA-MFSD method performs worse. In addition we find that the backward DMA-MFSD algorithm even outperforms the DFA-MFSD method in the computational complexity and precision. |
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