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Weighted multifractal analysis of financial time series

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Abstract

In this paper, we propose the weighted multifractal analysis based on variance-weighted partition function (WMA), to evaluate the fractals of nonlinear time series containing amplitude information. The reliability of the proposed WMA is supported by simulations on generated and real-world financial volatility data. Numerical simulations with synthesized data show that WMA is comparative to the classic partition function-based standard multifractal analysis (SMA) and the multifractal detrending moving average analysis. More importantly, empirical analyses of Chinese stock indices illustrate that WMA outperforms SMA in distinguishing Hang Seng Index form SSE Composite Index and SZSE Component Index qualitatively and quantitatively, showing the power of WMA in discriminating series with distinctive amplitudes.

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Acknowledgements

We thank the editor and the anonymous reviewers for their valuable suggestions and comments that helped the improvement of this article. The financial support by the Fundamental Research Funds for the Central Universities (2016YJS152) is gratefully acknowledged.

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  1. Department of Mathematics, School of Science, Beijing Jiaotong University, Beijing, 100044, People’s Republic of China

    Hui Xiong & Pengjian Shang

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  1. Hui Xiong
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  2. Pengjian Shang
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Correspondence to Pengjian Shang.

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Xiong, H., Shang, P. Weighted multifractal analysis of financial time series. Nonlinear Dyn 87, 2251–2266 (2017). https://doi.org/10.1007/s11071-016-3187-1

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