Abstract: At present, a large number of studies have confirmed the existence of multiple fractal characteristics in financial markets. The factors that lead to the existence of this phenomenon in the time series of financial markets include two main aspects: On the one hand, the thick-tailed distribution, and on the other hand, the different degrees of correlation between large and small fluctuations. The multiple fractals, which are caused by different degrees of volatility, can predict the future trend of asset prices to a certain extent. As a typical feature of financial markets, the impact of good and bad news shocks on asset price volatility is inconsistent, resulting in asymmetric multifractals. Therefore, if we can comprehensively analyze the asymmetric multifractal characteristics of market volatility, we can better understand the market laws and effectively avoid risks.
Considering that the time series of financial market may be affected by noise, and the empirical modal decomposition method of high and low frequency index values can effectively solve the problems of noise pollution, non-smoothness and heteroskedasticity after reconstructing the series. Therefore, based on the empirical modal decomposition method, this paper decomposes and reconstructs the series into high and low frequency series, followed by using the quadratic function to portray the dynamic trend of the market, and proposes for the first time to use the quadratic and primary coefficients as the proxy variables of “positive and negative volatility” to classify the three trends of up, oscillation and down, and proposes a new EMD based on the traditional MF-DCCA. A new EMD-MF-DCCA method is proposed to measure the asymmetric multiple fractal correlation of financial markets under the three trends of upward, oscillation and downward. Theoretically, the EMD-MF-DCCA method can portray the asymmetric multifractal correlations of financial markets under different volatility zone trends, and compared with the traditional MF-DCCA method, the EMD-MF-DCCA method is more accurate in portraying the multifractals under different volatility degrees.
Taking Shanghai and Shenzhen stock markets as the research object, the daily trading data are obtained from “Tongdaxin” trading software. The data interval is from January 4, 2010 to March 19, 2020, and the closing price data of 2418 trading days are obtained. The empirical results show that: During the period of oscillation and decline, the two markets are characterized by long-term correlation in large fluctuations and anti-persistence in small fluctuations, with asymmetric multifractal relationship; In the rising period, there is a multifractal relationship between the two markets with time-varying fluctuations; Compared with the traditional MF-ADCCA method, EMD-MF-DCCA method can describe the multifractal strength of the market more accurately. The above research results provide reasonable suggestions for further studying the complex asymmetric dependence between markets.

Key words: high and low frequency index values, EMD, MF-DCCA method, multifractal, asymmetry, up-down trend

摘要： 本文基于经验模态分解的高低频索引值重构序列,提出了一种新的EMD-MF-DCCA方法来度量上涨、振荡、下跌三种趋势下金融市场的非对称多重分形相关性。以沪深股市为研究对象,结果发现:在振荡和下跌时期,两市场间在大波动时呈现长呈相关性特征,在小波动时呈现反持续性特征,具有非对称多重分形关系;在上涨时期,两市场间存在时变波动的多重分形关系;与传统MF-ADCCA法相比,EMD-MF-DCCA法能更准确的刻画市场的多重分形强度。上述研究成果为深入研究市场间复杂的非对称依赖关系提供了合理的建议。

关键词: 高低频索引值, EMD, MF-DCCA方法, 多重分形, 非对称性, 涨跌趋势