Wang Hanqing, Wang Jun, Wang Guochao
Department of Mathematics, School of Science, Beijing Jiaotong University, Beijing 100044, People's Republic of China.
Chaos. 2018 Aug;28(8):083122. doi: 10.1063/1.5020235.
The exploration of return volatility dynamics is of great significance to evaluate investment risk, avoid stock market crisis, and purchase stock portfolio. In this paper, we propose a novel concept to characterize the fluctuation duration of stock markets, which is continuous fluctuation intensity (CFI). The CFI represents the duration for continuous increasing or decreasing return volatilities (or normalized absolute returns) above or below a previous day's value. Distinguished from previous studies, the CFI does not need to set a threshold in advance but to select the sequence of return volatilities that are continuously growing or falling in the series. So, the research on continuous fluctuation intensity is a new approach in return volatility study. For investigating the nonlinear properties of CFI, probability distribution, autocorrelation analysis, and scatterplot analysis are utilized for the empirical data from China and USA stock markets. Besides, fractional sample entropy and fuzzy entropy are employed to explore the complexity of CFI series. Then, some meaningful results of CFI series are acquired, which manifest that the study of the proposed concept is feasible and valuable. Moreover, we do the same investigations for return volatility series to explore the similarities and differences between CFI series and volatility series.
探索收益率波动率动态对于评估投资风险、避免股市危机以及构建股票投资组合具有重要意义。在本文中，我们提出了一个新颖的概念来刻画股票市场的波动持续时间，即连续波动强度（CFI）。CFI表示收益率波动率（或标准化绝对收益率）连续高于或低于前一日值的持续时间。与以往研究不同的是，CFI不需要预先设定阈值，而是从序列中选择连续上升或下降的收益率波动率序列。因此，对连续波动强度的研究是收益率波动率研究中的一种新方法。为了研究CFI的非线性特性，我们对中国和美国股票市场的实证数据进行了概率分布、自相关分析和散点图分析。此外，还采用了样本熵和模糊熵来探究CFI序列的复杂性。然后，我们得到了一些关于CFI序列的有意义的结果，这些结果表明所提出概念的研究是可行且有价值的。此外，我们对收益率波动率序列进行了同样的研究，以探索CFI序列与波动率序列之间的异同。
