Tian Qiang, Shang Pengjian, Feng Guochen
Department of Mathematics, School of Science, Beijing Jiaotong University, Beijing, 100044 People's Republic of China.
Nonlinear Dyn. 2016;85(4):2635-2652. doi: 10.1007/s11071-016-2851-9. Epub 2016 May 26.
Similarity in time series is an important feature of dynamical systems such as financial systems, with potential use for clustering of series in system. Here, we mainly introduce a novel method: the reconstructed phase space information clustering method to analyze the financial markets. The method is used to examine the similarity of different sequences by calculating the distances between them, which the main difference from previous method is the way to map the original time series to symbolic sequences. Here we make use of the state space reconstruction to construct the symbolic sequences and quantify the similarity of different stock markets and exchange rate markets considering the chaotic behavior between the complex time series. And we compare the results of similarity of artificial and real data using the modified method, information categorization method and system clustering method. We conclude that the reconstructed phase space information clustering method is effective to research the close relationship in time series and for short time series especially. Besides, we report the results of similarity of different exchange rate time series in different periods and find the effect of the exchange rate regime in 2008 on the time series. Also we acquire some characteristics of exchange rate time series in China market, especially for the top four trading partners of China.
时间序列的相似性是金融系统等动态系统的一个重要特征，在系统中对序列进行聚类具有潜在用途。在此，我们主要介绍一种新颖的方法：重构相空间信息聚类方法来分析金融市场。该方法通过计算不同序列之间的距离来检验它们的相似性，与先前方法的主要区别在于将原始时间序列映射到符号序列的方式。在这里，我们利用状态空间重构来构建符号序列，并考虑复杂时间序列之间的混沌行为来量化不同股票市场和汇率市场的相似性。并且我们使用改进方法、信息分类方法和系统聚类方法比较人工数据和真实数据的相似性结果。我们得出结论，重构相空间信息聚类方法对于研究时间序列中的紧密关系是有效的，尤其是对于短时间序列。此外，我们报告了不同时期不同汇率时间序列的相似性结果，并发现2008年汇率制度对时间序列的影响。我们还获得了中国市场汇率时间序列的一些特征，特别是对于中国的前四大贸易伙伴。
