Wang Guochao, Wang Jun
Department of Mathematics, School of Science, Beijing Jiaotong University, Beijing 100044, People's Republic of China.
Chaos. 2017 Jan;27(1):013117. doi: 10.1063/1.4974216.
We make an approach on investigating the fluctuation behaviors of financial volatility duration dynamics. A new concept of volatility two-component range intensity (VTRI) is developed, which constitutes the maximal variation range of volatility intensity and shortest passage time of duration, and can quantify the investment risk in financial markets. In an attempt to study and describe the nonlinear complex properties of VTRI, a random agent-based financial price model is developed by the finite-range interacting biased voter system. The autocorrelation behaviors and the power-law scaling behaviors of return time series and VTRI series are investigated. Then, the complexity of VTRI series of the real markets and the proposed model is analyzed by Fuzzy entropy (FuzzyEn) and Lempel-Ziv complexity. In this process, we apply the cross-Fuzzy entropy (C-FuzzyEn) to study the asynchrony of pairs of VTRI series. The empirical results reveal that the proposed model has the similar complex behaviors with the actual markets and indicate that the proposed stock VTRI series analysis and the financial model are meaningful and feasible to some extent.
我们对金融波动持续时间动态的波动行为进行了研究。提出了一个新的波动双组分范围强度（VTRI）概念，它由波动强度的最大变化范围和持续时间的最短通过时间组成，能够量化金融市场中的投资风险。为了研究和描述VTRI的非线性复杂特性，通过有限范围相互作用的有偏投票者系统建立了一个基于随机主体的金融价格模型。研究了收益时间序列和VTRI序列的自相关行为以及幂律标度行为。然后，通过模糊熵（FuzzyEn）和Lempel-Ziv复杂度分析了真实市场和所提出模型的VTRI序列的复杂性。在此过程中，我们应用交叉模糊熵（C-FuzzyEn）来研究VTRI序列对的异步性。实证结果表明，所提出的模型具有与实际市场相似的复杂行为，并且表明所提出的股票VTRI序列分析和金融模型在一定程度上是有意义和可行的。
