时间序列相空间重构数据挖掘方法及其在证券市场的应用
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摘要
金融市场是融通资金的场所。金融市场实现了投资需求和筹资需求的对接,能有效的化解资本的供求矛盾。金融投资分析方法一直是金融领域的研究热点。随着金融市场的飞速发展,投资分析方法也得到不断的创新和进步。传统的时间序列模型的应用一方面依赖于某些假设条件,因而应用受到限制;另一方面,由于经济和商业时间序列的结构经常是逐渐变化的,应用结构固定的全局模型来描述并不十分合适。
随着信息技术在金融行业的普及以及人们收集数据能力的大幅提高,在金融市场的飞速发展过程中,积累了海量的包含丰富信息的数据。数据挖掘方法为人们分析金融时间序列提供了新的思路和视野。本文以相空间重构技术为基础,以时间序列作为研究对象,分析面向时间序列数据的数据挖掘方法,并将研究结果应用于实际金融市场,以发现金融时间序列中隐含的规律、模式和知识,为市场分析和投资决策提供新的思路、方法和辅助决策信息。
本文从研究所处的背景出发,详细讨论了数据挖掘技术以及时间序列数据挖掘与金融数据挖掘的相关研究现状,并分析了相空间重构的相关理论和方法。为应用相空间重构进行时间序列数据挖掘的可行性提供了理论基础和技术保障。
通过对比时间序列模式挖掘的不同思路,本文指出时间序列数据挖掘框架TSDM所存在的问题。系统地提出了应用小波聚类进行序列时间模式挖掘的方法。应用小波变换的多分辨率特性和基于网格的划分方法,可以实现任意形状和不同精度的聚类。采用以事件指导的投资策略将方法应用于中国证券市场。结果表明,以时间模式预测事件为指导的投资策略能获得高于持有策略的收益;时间模式挖掘能有效识别事件点;事件序列与非事件序列存在显著差别。
在讨论了嵌入定理和时间序列的可预测性的基础上,本文从现有模糊神经网络存在的问题入手,结合非线性的空间聚类方法EM算法,对原有TS模糊神经网络模型进行改进,提出了基于相空间重构的EM聚类模糊神经网络预测模型。通过对重构空间进行EM模糊聚类,实现数据对象的分类训练以及隶属度的计算,以减少输入规则的条数简化神经网络的结构。同时,将该模型分别应用于深成指数和上证指数。结果表明,该预测模型的预测误差低于传统的BP模型,有效地提高了预测精度。
本文从序列异常的角度提出了时间序列的偏差异常检测方法。应用CC算法同时对嵌入维和嵌入延时进行估计进行重构以构造多维空间,应用偏差异常检测方法抽取异常模式,再通过符号离散化将问题转化为分类问题构建决策树实现异常的分类和预测。以决策树的分类标识为指导构建交易策略,在证券市场上进行了应用。结果表明,尽管在股市大势呈现下降趋势的情况下,应用分类标识为指导的交易策略仍能获得较高的收益。
本文应用相空间重构技术将时间序列分割成长度相同的子序列集合,并将其映射到多维特征空间,从而将有序的时间序列一维数据挖掘问题转换成为多维空间的无序数据集合的挖掘问题。本文的研究不仅为金融时间序列分析提供了新的方法,也为数据挖掘技术提供了新的研究思路。
Financial market sets up a connection between the demands of investment and funding. It could resolve the contradiction between supply and demand of capital effectively. Analysis methods of investment are always the researching hotspot of financial field. With the rapid developments of the financial market, there comes lots of creation and progress in investment analysis. Traditional time sires models have two disadvantages, which could not be avoided. The one is that it depends on several hypothesis conditions. The other is that applying overall fixed model to describe the economic or commercial time series structures, which are changed with times gradually, is not perfectly applicable.
With the popularization of information technology in financial field and significant improvement of people’s ability of collecting data, large amounts of data were accumulated, which were full of abundant information, while the rapid development of financial market. Data mining provides us new directions to analyze financial time series. Based on phase space reconstruction, This paper took time series as researching object to present time series data mining methods and apply these methods to financial market, in order to find the implicit rules, patterns and knowledge, so as to provide new directions, methods and accessorial information to market analysis and investment decision.
Considering the researching background, this paper discussed the associated research of data mining technology, time series and financial time series data mining, separately. As following, the basic theory and methods of phase space reconstruction were analyzed in details. All of these provided the theoretical basis and technical feasibility to time series data mining based on phase space reconstruction.
After contrasting the different means of time series pattern mining, we pointed out the problem of time series data mining framework TSDM, and presented the temporal patterns mining method based Wave Cluster systematically. By the multiresolution property of wavelet transformations and the grid-based partition method, it could detect arbitrary-shape clusters at different scales and levels of detail. We set up the investment strategy dictated by events that was predicted from temporal patterns and applied it to Chinese stock market. The result shows it would get the yield higher than buy-and-hold strategy. There is significant difference between the event series and non-event series. Mining temporal pattern could identify event effectively.
After discussing the embedding theory and the time series forecasting, we improved original TS fuzzy neural network by means of EM (Expectation Maximization) method that is applicable to nonlinear space’s clustering, and presented a new forecasting model of fuzzy neural network combined with Expectation Maximization method based on phase space reconstruction. It could cluster the data object and compute the membership automatically, to reduce the number of rules and simplify the structure of neural networks by applying EM method to the input reconstructed space. We used it to make forecasts on stock market. The results show that this model could reduce the error of forecasts effectively and improve the system’s performance.
We presented the sequential deviation detection method of time series derived from sequential outlier. We applied phase reconstruction CC method to estimate embedded dimension and embedded delay of time series and mapped time series into multi-dimension space. Extracted from multi-dimension phase space by the method of sequential deviation detection, outlier set was used to construct a decision tree in order to identify the kinds of outliers. According to the results of decision tree, a trading strategy was set up and applied it to Chinese stock market. The results show that, although in bear market, the strategy dictated by decision tree brought in considerable yield.
This paper divided time series into the sub-series set which had the same length and mapped all these sub-series into multidimensional space, so as to turn the one dimensional ordered data problem of time series into data mining on out-of-order data sets of multidimensional space. The researches of the paper provided not only new methods to financial time series analysis, but also new directions to data mining research.
随着信息技术在金融行业的普及以及人们收集数据能力的大幅提高,在金融市场的飞速发展过程中,积累了海量的包含丰富信息的数据。数据挖掘方法为人们分析金融时间序列提供了新的思路和视野。本文以相空间重构技术为基础,以时间序列作为研究对象,分析面向时间序列数据的数据挖掘方法,并将研究结果应用于实际金融市场,以发现金融时间序列中隐含的规律、模式和知识,为市场分析和投资决策提供新的思路、方法和辅助决策信息。
本文从研究所处的背景出发,详细讨论了数据挖掘技术以及时间序列数据挖掘与金融数据挖掘的相关研究现状,并分析了相空间重构的相关理论和方法。为应用相空间重构进行时间序列数据挖掘的可行性提供了理论基础和技术保障。
通过对比时间序列模式挖掘的不同思路,本文指出时间序列数据挖掘框架TSDM所存在的问题。系统地提出了应用小波聚类进行序列时间模式挖掘的方法。应用小波变换的多分辨率特性和基于网格的划分方法,可以实现任意形状和不同精度的聚类。采用以事件指导的投资策略将方法应用于中国证券市场。结果表明,以时间模式预测事件为指导的投资策略能获得高于持有策略的收益;时间模式挖掘能有效识别事件点;事件序列与非事件序列存在显著差别。
在讨论了嵌入定理和时间序列的可预测性的基础上,本文从现有模糊神经网络存在的问题入手,结合非线性的空间聚类方法EM算法,对原有TS模糊神经网络模型进行改进,提出了基于相空间重构的EM聚类模糊神经网络预测模型。通过对重构空间进行EM模糊聚类,实现数据对象的分类训练以及隶属度的计算,以减少输入规则的条数简化神经网络的结构。同时,将该模型分别应用于深成指数和上证指数。结果表明,该预测模型的预测误差低于传统的BP模型,有效地提高了预测精度。
本文从序列异常的角度提出了时间序列的偏差异常检测方法。应用CC算法同时对嵌入维和嵌入延时进行估计进行重构以构造多维空间,应用偏差异常检测方法抽取异常模式,再通过符号离散化将问题转化为分类问题构建决策树实现异常的分类和预测。以决策树的分类标识为指导构建交易策略,在证券市场上进行了应用。结果表明,尽管在股市大势呈现下降趋势的情况下,应用分类标识为指导的交易策略仍能获得较高的收益。
本文应用相空间重构技术将时间序列分割成长度相同的子序列集合,并将其映射到多维特征空间,从而将有序的时间序列一维数据挖掘问题转换成为多维空间的无序数据集合的挖掘问题。本文的研究不仅为金融时间序列分析提供了新的方法,也为数据挖掘技术提供了新的研究思路。
Financial market sets up a connection between the demands of investment and funding. It could resolve the contradiction between supply and demand of capital effectively. Analysis methods of investment are always the researching hotspot of financial field. With the rapid developments of the financial market, there comes lots of creation and progress in investment analysis. Traditional time sires models have two disadvantages, which could not be avoided. The one is that it depends on several hypothesis conditions. The other is that applying overall fixed model to describe the economic or commercial time series structures, which are changed with times gradually, is not perfectly applicable.
With the popularization of information technology in financial field and significant improvement of people’s ability of collecting data, large amounts of data were accumulated, which were full of abundant information, while the rapid development of financial market. Data mining provides us new directions to analyze financial time series. Based on phase space reconstruction, This paper took time series as researching object to present time series data mining methods and apply these methods to financial market, in order to find the implicit rules, patterns and knowledge, so as to provide new directions, methods and accessorial information to market analysis and investment decision.
Considering the researching background, this paper discussed the associated research of data mining technology, time series and financial time series data mining, separately. As following, the basic theory and methods of phase space reconstruction were analyzed in details. All of these provided the theoretical basis and technical feasibility to time series data mining based on phase space reconstruction.
After contrasting the different means of time series pattern mining, we pointed out the problem of time series data mining framework TSDM, and presented the temporal patterns mining method based Wave Cluster systematically. By the multiresolution property of wavelet transformations and the grid-based partition method, it could detect arbitrary-shape clusters at different scales and levels of detail. We set up the investment strategy dictated by events that was predicted from temporal patterns and applied it to Chinese stock market. The result shows it would get the yield higher than buy-and-hold strategy. There is significant difference between the event series and non-event series. Mining temporal pattern could identify event effectively.
After discussing the embedding theory and the time series forecasting, we improved original TS fuzzy neural network by means of EM (Expectation Maximization) method that is applicable to nonlinear space’s clustering, and presented a new forecasting model of fuzzy neural network combined with Expectation Maximization method based on phase space reconstruction. It could cluster the data object and compute the membership automatically, to reduce the number of rules and simplify the structure of neural networks by applying EM method to the input reconstructed space. We used it to make forecasts on stock market. The results show that this model could reduce the error of forecasts effectively and improve the system’s performance.
We presented the sequential deviation detection method of time series derived from sequential outlier. We applied phase reconstruction CC method to estimate embedded dimension and embedded delay of time series and mapped time series into multi-dimension space. Extracted from multi-dimension phase space by the method of sequential deviation detection, outlier set was used to construct a decision tree in order to identify the kinds of outliers. According to the results of decision tree, a trading strategy was set up and applied it to Chinese stock market. The results show that, although in bear market, the strategy dictated by decision tree brought in considerable yield.
This paper divided time series into the sub-series set which had the same length and mapped all these sub-series into multidimensional space, so as to turn the one dimensional ordered data problem of time series into data mining on out-of-order data sets of multidimensional space. The researches of the paper provided not only new methods to financial time series analysis, but also new directions to data mining research.
引文
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