时间序列相似度在股市日内交易数据的应用.pdf

摘 要 实际问题中的时间序列因其存在噪声，很难直接用于统计建模。而且经常 要处理的数据都是海量数据，需要计算机进行大规模的运算，效率低并且容错率 也低。类似于信号处理要对原始信号进行压缩，我们也要对原始时序数据进行一 定的压缩降维处理。 本文从股市 K 线系统中得到启示，用距离法找取一个高频时间序列的关键 点集合，用关键点集合来代替原始时序，这样做既能保留原高频时序的主要趋势， 去除掉一些不重要的噪声扰动，又能降低对时序的存储，减少运算复杂度。 时间序列聚类的一个最关键问题是时序距离的定义，传统的一些时序定义 都仅从观测值表面入手，在实际应用中都存在一些弊端。考虑到实际影响股市的 因素并不容易被直接观测到，我们能观测到的仅是股市的点位，所以本文采用隐 马氏链模型对股市日内数据进行拟合。接着把 Kullback Leibler 距离进行推广到 两个隐马氏链模型之间的距离。有了时序距离度量之后，采用分层次聚类法对股 市日内数据进行聚类，最后得出类别之间跳跃的转移概率矩阵。 关键词：距离法；Level2 高频数据；隐马氏链模型；K-L 距离 Abstract This paper applies the distance measure method, which stems from candlesticks system of stock market, to get the keypoints for each intraday trading data. The keypoints set can represent the major trend of the original data. By implementing this process, we can reduce the complexity of the statistical modeling and save data storing cost. The distance between time series is the key point in time series clustering. The conventional distances only study on the observation data, and have some defects in the real application. Considering the determinative factor of the stock market can not be directly observed, it is reasonable to apply the Hidden Markov Model(HMM) to the modeling of the Intraday trading data. Furthermore, we can use the Kullback Leibler distance to measure the distance between two HMM. In other words, we get the distance between two intraday trading time series. Finally, we can complete clustering of intraday trading data time series, and we can get the transition probability from one cluster to other clusters as well. The trasition matrix can help the investors to master the intraday trend. Key words: Distance measure; level2 high frequency data; Hidden Markov Model, Kullback Leibler distance