CONVERGENCE INVESTIGATION OF MULTIFRACTAL ANALYSIS BASED ON Lp-NORM CONSTRAINT

Jian Wang (), Wenjing Jiang and Wei Shao
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Jian Wang: School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, P. R. China
Wenjing Jiang: School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, P. R. China
Wei Shao: ��School of Economics, Nanjing University of Finance and Economics, Nanjing 210023, P. R. China

FRACTALS (fractals), 2022, vol. 30, issue 06, 1-14

Abstract: In this paper, we propose the multifractal detrending fluctuation analysis based on Lp-norm constrain (MF-DFN). We assess the performance of the proposed algorithm by constructing a p-model based multiplicative cascades time series. We calculate the generalized Hurst exponent H(q), Rényi exponent τ(q), singularity exponent α and multifractal spectrum f(α) for multifractal detrended fluctuation analysis (MF-DFA) and MF-DFN, respectively. We notice that under different norm constraints, the distribution of multifractal characteristics is quite different. Appropriate norm constraints can make the multifractal characteristics of time series described more accurately. Based on the analytical solution curve, the distribution of different multifractal numerical curves determines the correct selection of norm constraint value. In this study, using a combination of norms 0.01 and 4, the depicted numerical curves almost overlap the theoretical curve, which shows that the proposed MF-DFN is superior to MF-DFA. To eliminate the influence of specific time series, we reset parameters nmax and P1 in p-model. Various experimental results also show the effectiveness of the proposed MF-DFN. In addition, we also verify the efficiency of the proposed MF-DFN by using the practical application. The experimental results show that our proposed method plays a significant role in ECG classification.

Keywords: Multifractal; Lp-Norm; Multiplicative Cascades; p-Model (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0218348X2250116X

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