基于改进样本熵的金融时间序列复杂性研究

Research on Financial Time Series Complexity Based on Modified Sample Entropy

金融时间序列的复杂度分析对研究金融市场的内在规律性具有重要意义。但是,复杂度衡量方法样本熵在以往的实验中,被证实熵值的大小并不总是和序列的复杂度相关。样本熵在计算时间序列复杂度时,没有考虑到序列中相似向量的分布以及构成序列向量的复杂性对时间序列复杂度的影响。针对这个问题,在样本熵的基础上提出了二维熵。该方法的创新性主要体现在:二维熵在计算序列中向量的自相似性概率时,向量之间的相似性不仅取决于向量之间的模式距离,还和两个向量之间的时间距离有关;二维熵熵值的大小不仅和两种模式下向量的自相似概率的条件概率值有关,还和模式自相似概率的值相关。通过模拟时间序列证实了二维熵的有效性及优越性,最后将二维熵以及互二维熵应用在四只金融股指序列中,衡量它们之间的复杂度关系。发现中国市场的两只股指的复杂度在不同时间段的趋势是一致的,并且其异步性相对其他股指也是最小的。美股和港股的复杂度在不同时间段趋势大致也是一样的,且两者的异步性相对中国市场的两个股指也是相对较小的。

The complexity analysis of financial time series is of great significance to the study of the inherent regularity of the financial markets.However,it has been proved that the entropy of sample in the complexity measurement method is not always related to the complexity of the time series in previous experiments.In fact,when calculating the complexity of time series,the sample entropy does not consider the effect that the distribution of similar vectors in the time series and the complexity of the vectors on the complexity of time series.For this,we propose two dimensional entropy based on sample entropy.The innovation of this method is mainly reflected in the following aspects:when calculating the probability of self-similarity of vectors in a time series,the similarity between vectors depends on not only the pattern distance between the vectors,but also the time distance between two vectors.The entropy value of two dimensional entropy is not only related to the conditional probability value of the self-similar probability of the vector in the two pattern lengths,but also related to the value of the self-similarity probability of the pattern.Through several simulated time series,the validity and advantages of the two dimensional entropy advantages are proved.Finally,two dimensional entropy and cross two dimensional entropy are applied to four financial index series,and the complexity relationship between them is measured.It is found that the complexity of the two stock indexes in the Chinese market is consistent in different time periods,and its asynchronism is also the smallest relative to other stock indexes.The complexity of US stock and Hong Kong stock is roughly the same in different time periods,and the asynchrony between them is relatively small compared with the two indexes in Chinese market.