MULTIFRACTAL ANALYSIS WITH DETRENDING WEIGHTED AVERAGE ALGORITHM OF HISTORICAL VOLATILITY

Jian Wang () 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
Wei Shao: School of Economics, Nanjing University of Finance and Economics, Nanjing 210023, P. R. China

FRACTALS (fractals), 2021, vol. 29, issue 05, 1-11

Abstract: In this paper, we develop the multifractal detrending weighted average algorithm of historical volatility (MF-DHV) for one-dimensional multifractal measure based on the classical multifractal detrended fluctuation analysis (MF-DFA). In the calculation process of getting a local trend for MF-DHV, historical volatility is taken to develop an moving average algorithm, which is different from the simple moving average function in multifractal detrended moving average (MF-DMA). We assess the performance of three methods such as MF-DFA, MF-DMA, and MF-DHV based on the p-model multiplicative cascading constructed time series. The computational results show that all the estimated generalized Hurst exponent H(q), the scaling exponent τ(q), and the singularity spectrum f(α) of MF-DHV are in good agreement with the theoretical values. In addition, we also calculate the standard deviations of Herr and τerr for three methods, and the lowest errors in MF-DHV provides the most accurate estimates. To avoid the accidental selection of parameters, we change the total length of the generated multifractal simulation data and p-value, respectively. It is found that in all the cases, the MF-DHV outperforms the other two methods.

Keywords: MF-DHV; MF-DFA; MF-DMA; p-Model (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (3)

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DOI: 10.1142/S0218348X21501930

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