基于标度理论的股指时间序列相似性分析

Similarity Analysis of Stock Indices Time Series Based on Scale Theory

股指时间序列的相似性分析是当前金融学研究的热点之一。为了提高股指时间序列相似性分析的准确度,从标度不变性、多重分形及波动聚集性三个层面定义了标度理论的度量指标,并基于此对股指序列进行表示。将分割后的每一序列子区间看作时间点,则分割、表示后的不同股指序列构成一个多指标的面板数据。基于面板数据特征及指标相对重要性,提出了一种新型的多指标面板数据相似性度量函数——复合距离函数,用以度量股指时间序列的相似性。聚类结果表明,相较于其他两种方法,基于标度理论和复合距离函数的相似性度量方法能够显著提高相似性度量的准确度,同时具有较强的稳健性。

Similarity analysis of stock indices time series is one of the key research contents in financial studies . In order to improve the accuracy of stock indices time series similarity analysis , we define the metrics indexes of scale theory based on scale invariance , multifractal character , and volatility clustering .Stock indices time series are represented by the three indices .If the segmentation is viewed as a time point , the stock indices time series split and expressed will constitute a multivariable panel data .Based on the features of panel data and the relative importance of these indicators , we put forward a new similarity measurement function , the complex-distance-function , to analyse the similarity of stock indices time series .Clustering results indicate that , compared with the two other methods , the similarity analysis based on scale theory and complex-distance-function can improve the accuracy of the analysis result significantly with strong robustness .