Weighted multifractal cross-correlation analysis based on Shannon entropy

Abstract

a b s t r a c tIn this paper, we propose a modification of multifractal cross-correlation analysis based on statistical moments (MFSMXA) method, called weighted MFSMXA method based on Shannon entropy (W-MFSMXA), to investigate cross-correlations and cross-multifractality between time series. Robustness of this method is verified by numerical experiments with both artificial and stock returns series. Results show that the proposed W-MFSMXA method not only keep the multifractal structure unchanged, but contains more significant information of series compared to the previous MFSMXA method. Furthermore, analytic formulas of the binomial multifractal model are generated for W-MFSMXA. Theoretical analysis and finite-size effect test demonstrate that W-MFSMXA slightly outperforms MFSMXA for relatively shorter series. We further generate the scaling exponent ratio to describe the relation of two methods, whose profile is found approximating a centrosymmetric hyperbola. Cross-multifractality is found in returns series but then destroyed after being shuffled as a consequence of the removed long memory in separate series.

Joint multifractal analysis based on the partition function approach: analytical analysis, numerical simulation and empirical application

“…The daily return time series of the two indexes are shown in figure S1 (see supplementary data). functions are not monotonic with respect to p or q. a a ( ) These empirical findings suggest that the cross correlations between daily volatilities of DJIA and NASDAQ possess multifractal nature, which is consistent with previous results using the MF-X-DFA, MF-X-DMA and MF-X-PF q ( ) methods [26,28,41,72].…”

Complexity and uncertainty analysis of financial stock markets based on entropy of scale exponential spectrum

“…where 0 < p < 0.5, n(k) is the number of digits equal to 1 in the binary representation of index k [45]. In this paper, we choose p = 0.2, 0.3, 0.4 and the length is 2 16 .…”

Multifractal analysis of financial markets

“…Xiong and Shang proposed the weighted MF-X-PF(q) method (W-MFSMXA) [391]. Their numerical experiments on two-exponent ARFIMA processes, binomial measures and NBVP time series illustrate that W-MFSMXA slightly outperforms MF-X-PF(q) for relatively short time series.…”

“…The joint multifractal nature between two volatility time series has also been investigated. For stock market indices, some studies have been done on the pair of daily DJIA and NASDAQ from July 1993 to November 2003 [141], the pair of daily A-share and B-share market indices in Shanghai and Shenzhen from 2 January 1996 to 1 April 2010 [865], the pair of daily SSEC and SZCI from 4 April 1991 to 13 April 2009 [422] and from 4 January 2002 to 31 December 2008 [108], the six pairs of daily SSEC, SZCI, DJIA and NASDAQ from 18 May 1995 to 18 May 2015 using MF-X-PF [829], and the pair of daily DJIA and NASDAQ from 2 January 1997 to 29 December 2014 using MF-X-PF [391].…”