基于重标级差分析的时间序列分割方法

针对重标级差分析法（Rescaled Range Analysis,R/S）在时间序列挖掘中的应用,提出了一种基于R/S分析的时间序列分割模型和算法,该算法能够根据序列波动的聚集性和自相似的特征,将序列分割为多个子序列。实验结论表明该方法可以发现时间序列的波动变化规律,方法有效、正确。     

基于分割模式的时间序列矢量符号化算法

针对符号化聚合近似算法(SAX)中时间序列必须等长分割的缺陷,提出一种基于分割模式的时间序列符号化算法(SMSAX)。利用三角阈值法对随机抽样的时间序列进行特征提取,计算时间序列最大压缩比,将其作为时间窗宽提取分割点,进而求出时间序列的分割模式。利用得到的分割模式对时间序列进行分割降维,通过均值和波动率对分割后的子序列进行向量符号化。根据时间序列特征对其进行不等长分割,并加入波动率消除奇异点的影响。实验结果表明,SMSAX能获得比SAX更精确的结果。     

有监督时间序列分割与状态识别算法

时间序列分割与状态识别是一项重要的时间序列挖掘任务,可用于识别被监测对象的运行状态,然而目前多数无监督时间序列分割算法得到的结果无法满足用户的状态识别期望。为实现符合用户意图的时间序列分割,提出一种有监督的时间序列分割算法。构造特征集合并自动训练特征概率模型参数,以此构建特征高斯概率分布模型进行相关序列的特征设计,同时利用匹配损失计算和改进的贪心策略设定特征权重约束,通过增加分割位置约束条件及增量计算2种优化方式提高分割效率。在多个真实数据集上的实验结果表明,与pHMM和AutoPlait算法相比,该算法可以全面表达状态类别,对时间序列进行更精准的分割。     

基于HTM的遗传时间序列分割算法

结合层级实时记忆（Hierarchical Temporal Memory,HTM）模型与基于模式集的遗传时间序列分割算法各自的优点,用基于HTM的适应值函数替换原基于模式集的适应值函数,提出基于HTM的遗传时间序列分割算法。该算法可实现时间序列的分割及其相应子序列的分类识别。同时,针对HTM对训练样本的要求,提出一种基于模式集的HTM训练样本生成算法。最后在股票序列上验证了这2种算法的有效性。      

基于自适应增量集成学习的非平稳金融时间序列预测

金融市场对于社会经济的发展非常重要,因此金融时间序列预测（Financial time series prediction, FTSP）一直是人们研究的焦点。至今,许多基于统计分析和软计算的方法被提出以解决FTSP问题,其中大多数方法将金融时间序列（Financial time series, FTS）视为或转化为平稳序列进行处理。但是,由于绝大部分FTS是非平稳的,因此这些方法通常存在伪回归或预测性能不佳等问题。本文提出了一种自适应增量集成学习（Self-adaptive incremental ensemble learning, SIEL）算法,用于解决非平稳金融时间序列预测（Non-stationary FTSP, NS-FTSP）问题。SIEL算法的主要思想是为每个非平稳金融时间序列（Non-stationary FTS, NS-FTS）子集增量地训练一个基模型,然后使用自适应加权规则将各基模型组合起来。SIEL算法的重点在于数据权重和基模型权重的更新：数据权重基于当前集成模型在最新数据集上的性能进行更新,其目的不是为了数据采样,而是为了权衡误差;基模型权重基于其所处环境进行自适应更新,且基模型在越新环境下的性能应具有越高的权重。此外,针对NS-FTS的特征,SIEL算法提出了一种能协调新旧知识以及应对环境重演的策略。最后,给出了SIEL算法在3个NS-FTS数据集上的实验结果,并将其与已有算法进行了对比。实验结果表明,SIEL算法能很好地解决NS-FTSP问题。     

时间序列相似性半监督谱聚类

时间序列相似度是时间序列数据挖掘的重要研究方向之一。如何利用时间序列相似度对提高时间序列数据聚类有着重要的意义。提出一种基于时间序列相似度的半监督谱聚类算法,通过选取适当的时间序列特征构造相似度与距离,在谱聚类算法的基础上利用标签数据选取初始类簇。实验表明,该算法使具有相似特征的时间序列可以很有效地被聚集到同一类中。     

基于云模型重叠度的相似性度量

云模型相似性是用来度量同类概念不同语言值的多个云之间关联程度的方法,相似云及其度量分析方法的提出是对云模型理论的扩展。针对目前相似性度量方法中时间复杂度过高和结果不稳定等不足,提出了一种基于云模型重叠度的相似性度量算法。首先,根据云模型期望、熵、超熵三个数字特征,定义两个云模型的位置关系和逻辑关系;其次,利用两个云的位置和形状特性,计算得到它们间的重叠度;最后,结合云模型重叠度与相似度的关系,将云模型的相似性度量转化为相应重叠部分的定量化描述。通过对时间序列分类实例的应用,验证了该算法在保证结果稳定度和正确率的前提下,与目前时间消耗较低的云模型相似度计算方法(LICM)相比,计算复杂度降低了50%,表明该算法具有可行性和有效性。     

基于可变模型的腹主动脉瘤分割算法

提出了一种基于可变模型的腹主动脉瘤分割算法。它利用相邻两个切片间的相关性以及医学先验知识,可以快速地分割腹主动脉瘤CTA图像序列,并且结果与专家人工分割结果接近。本文将像素点分为三类：边界内,边界点,边界外,这样就直接决定了模型形变方向,大大提高了分割效率。     

基于滑动窗口及局部特征的时间序列符号化方法

针对时间序列的数据挖掘将时间序列数据转换为离散的符号序列, 提出了一种基于滑动窗口及局部特征的时间序列符号化方法。该方法采用了滑动窗口的方法将时间序列分割, 每个分段采用多个斜率表示, 最后采用K-均值聚类算法对斜率表示的分段进行聚类, 实现时间序列的符号化。实验证明了该方法的有效性与准确性。     

多变量时间序列例外模式的识别

多变量时间序列(MTS)在金融、医学、科学、工程等领域是非常普遍的.本文提出一种在MTS中识别异常模式的方法.采用自底向上的分割算法将MTS分割成互不重叠的子序列,使用扩展的Frobenius范数来计算2个MTS子序列之间的相似性,通过K-均值聚类将MTS子序列分为若干个类.根据异常模式的定义,从这若干个类中识别出异常模式.在2个实际数据集上进行实验,实验结果验证算法的有效性.     

A support vector machine based MSM model for financial short-term volatility forecasting

Financial time series forecasting has become a challenge because of its long-memory, thick tails and volatility persistence. Multifractal process has recently been proposed as a new formalism for this problem. An iterative Markov-Switching Multifractal (MSM) model was introduced to the literature. It is able to capture many of the important stylized features of the financial time series, including long-memory in volatility, volatility clustering, and return outliers. The model delivers stronger performance both in- and out-of-sample than GARCH-type models in long-term forecasts. To enhance MSM’s short-term prediction accuracy, this paper proposes a support vector machine (SVM) based MSM approach which exploits MSM model to forecast volatility and SVM to model the innovations. To verify the effectiveness of the proposed approach, two stock indexes in the Chinese A-share market are chosen as the forecasting targets. Comparing with some existing state-of-the-art models, the proposed approach gives superior results. It indicates that the proposed model provides a promising alternative to financial short-term volatility prediction.     

Clustering heteroskedastic time series by model-based procedures

Financial time series are often characterized by similar volatility structures. The detection of clusters of series displaying similar behavior could be important in understanding the differences in the estimated processes, without having to study and compare the estimated parameters across all the series. This is particularly relevant when dealing with many series, as in financial applications. The volatility of a time series can be characterized in terms of the underlying GARCH process. Using Wald tests and the Autoregressive metrics to measure the distance between GARCH processes, it is shown that it is possible to develop a clustering algorithm, which can provide three classifications (with increasing degree of deepness) based on the heteroskedastic patterns of the time series. The number of clusters is detected automatically and it is not fixed a priori or a posteriori. The procedure is evaluated by simulations and applied to the sector indices of the Italian market.     

Bayesian estimation of the Gaussian mixture GARCH model

Bayesian inference and prediction for a generalized autoregressive conditional heteroskedastic (GARCH) model where the innovations are assumed to follow a mixture of two Gaussian distributions is performed. The mixture GARCH model can capture the patterns usually exhibited by many financial time series such as volatility clustering, large kurtosis and extreme observations. A Griddy-Gibbs sampler implementation is proposed for parameter estimation and volatility prediction. Bayesian prediction of the Value at Risk is also addressed providing point estimates and predictive intervals. The method is illustrated using the Swiss Market Index.     

Characteristic-Based Clustering for Time Series Data

With the growing importance of time series clustering research, particularly for similarity searches amongst long time series such as those arising in medicine or finance, it is critical for us to find a way to resolve the outstanding problems that make most clustering methods impractical under certain circumstances. When the time series is very long, some clustering algorithms may fail because the very notation of similarity is dubious in high dimension space; many methods cannot handle missing data when the clustering is based on a distance metric.This paper proposes a method for clustering of time series based on their structural characteristics. Unlike other alternatives, this method does not cluster point values using a distance metric, rather it clusters based on global features extracted from the time series. The feature measures are obtained from each individual series and can be fed into arbitrary clustering algorithms, including an unsupervised neural network algorithm, self-organizing map, or hierarchal clustering algorithm.Global measures describing the time series are obtained by applying statistical operations that best capture the underlying characteristics: trend, seasonality, periodicity, serial correlation, skewness, kurtosis, chaos, nonlinearity, and self-similarity. Since the method clusters using extracted global measures, it reduces the dimensionality of the time series and is much less sensitive to missing or noisy data. We further provide a search mechanism to find the best selection from the feature set that should be used as the clustering inputs.The proposed technique has been tested using benchmark time series datasets previously reported for time series clustering and a set of time series datasets with known characteristics. The empirical results show that our approach is able to yield meaningful clusters. The resulting clusters are similar to those produced by other methods, but with some promising and interesting variations that can be intuitively explained with knowledge of the global characteristics of the time series.     

Forecasting the volatility of stock price index

Accurate volatility forecasting is the core task in the risk management in which various portfolios’ pricing, hedging, and option strategies are exercised. Prior studies on stock market have primarily focused on estimation of stock price index by using financial time series models and data mining techniques. This paper proposes hybrid models with neural network and time series models for forecasting the volatility of stock price index in two view points: deviation and direction. It demonstrates the utility of the hybrid model for volatility forecasting. This model demonstrates the utility of the neural network forecasting combined with time series analysis for the financial goods.     

Symbolic complexity of volatility duration and volatility difference component on voter financial dynamics

The nonlinear complexity of volatility duration and volatility difference component based on voter financial dynamics is investigated in this paper. The statistic – volatility difference component is first introduced in this work, in an attempt to study the volatility behaviors comprehensively. The maximum change rate series and the average change rate series (both derived from the volatility difference components) are employed to characterize the volatility duration properties of financial markets. Further, for the proposed series model and the proposed financial statistic series (which are transformed to symbolic sequences), the permutation Lempel–Ziv complexity, a novel complexity measure, is introduced to study the corresponding randomness and complexity behaviors. Besides, Zipf analysis is also applied to investigate the corresponding Zipf distributions of the proposed series. The empirical study shows the similar complexity behaviors of volatility between the proposed price model and the real stock markets, which exhibits that the proposed model is feasible to some extent.     

标度曲线拟合与金融时间序列聚类

针对金融时间序列具有的多重分形特征,提出基于标度曲线测度沪深300指标股之间的相似性并实现聚类。该方法首先使用多标度退势波动分析(MSDFA)拟合不同自相关阶数下收益率序列的标度曲线,然后抽取其分布或形态特征构造模式向量。聚类通过含权K-means算法实现,最优类别数根据分类适确性指标(DBI)确定。结果显示,基于标度曲线的聚类能够揭示出股市的行业聚集性和板块间的关联性,在此基础上构造的投资组合可以显著降低风险,并且效果优于基于原始序列线性趋势特征的聚类。     

Volatility Trading ia Temporal Pattern Recognition in Quantised Financial Time Series

We investigate the potential of the analysis of noisy non-stationary time series by quantising it into streams of discrete symbols and applying finite-memory symbolic predictors. Careful quantisation can reduce the noise in the time series to make model estimation more amenable. We apply the quantisation strategy in a realistic setting involving financial forecasting and trading. In particular, using historical data, we simulate the trading of straddles on the financial indexes DAX and FTSE 100 on a daily basis, based on predictions of the daily volatility differences in the underlying indexes. We propose a parametric, data-driven quantisation scheme which transforms temporal patterns in the series of daily volatility changes into grammatical and statistical patterns in the corresponding symbolic streams. As symbolic predictors operating on the quantised streams, we use the classical fixed-order Markov models, variable memory length Markov models and a novel variation of fractal-based predictors, introduced in its original form in Tin_ o and Dorffner [1]. The fractal-based predictors are designed to efficiently use deep memory. We compare the symbolic models with continuous techniques such as time-delay neural networks with continuous and categorical outputs, and GARCH models. Our experiments strongly suggest that the robust information reduction achieved by quantising the real-valued time series is highly beneficial. To deal with non-stationarity in financial daily time series, we propose two techniques that combine ‘sophisticated’ models fitted on the training data with a fixed set of simple-minded symbolic predictors not using older (and potentially misleading) data in the training set. Experimental results show that by quantising the volatility differences and then using symbolic predictive models, market makers can sometimes generate a statistically significant excess profit. We also mention some interesting observations regarding the memory structure in the series of daily volatility differences studied.