Weighted multifractal analysis of financial time series

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.