Zhao Xiaojun, Liang Chenxu, Zhang Na, Shang Pengjian
School of Economics and Management, Beijing Jiaotong University, Beijing 100044, China.
School of Science, Beijing Jiaotong University, Beijing 100044, China.
Entropy (Basel). 2019 Jul 12;21(7):684. doi: 10.3390/e21070684.
Making predictions on the dynamics of time series of a system is a very interesting topic. A fundamental prerequisite of this work is to evaluate the predictability of the system over a wide range of time. In this paper, we propose an information-theoretic tool, multiscale entropy difference (MED), to evaluate the predictability of nonlinear financial time series on multiple time scales. We discuss the predictability of the isolated system and open systems, respectively. Evidence from the analysis of the logistic map, Hénon map, and the Lorenz system manifests that the MED method is accurate, robust, and has a wide range of applications. We apply the new method to five-minute high-frequency data and the daily data of Chinese stock markets. Results show that the logarithmic change of stock price (logarithmic return) has a lower possibility of being predicted than the volatility. The logarithmic change of trading volume contributes significantly to the prediction of the logarithmic change of stock price on multiple time scales. The daily data are found to have a larger possibility of being predicted than the five-minute high-frequency data. This indicates that the arbitrage opportunity exists in the Chinese stock markets, which thus cannot be approximated by the effective market hypothesis (EMH).
对系统时间序列的动态进行预测是一个非常有趣的话题。这项工作的一个基本前提是在广泛的时间范围内评估系统的可预测性。在本文中，我们提出了一种信息论工具，即多尺度熵差（MED），用于评估非线性金融时间序列在多个时间尺度上的可预测性。我们分别讨论了孤立系统和开放系统的可预测性。对逻辑斯谛映射、亨农映射和洛伦兹系统的分析证据表明，MED方法准确、稳健且具有广泛的应用。我们将新方法应用于中国股票市场的五分钟高频数据和日数据。结果表明，股票价格的对数变化（对数收益率）比波动率更难预测。交易量的对数变化在多个时间尺度上对股票价格对数变化的预测有显著贡献。发现日数据比五分钟高频数据更有可能被预测。这表明中国股票市场存在套利机会，因此不能用有效市场假说（EMH）来近似。
