金融多元时间序列挖掘方法研究与应用
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摘要
时间序列数据包括多元时间序列和一元时间序列两种数据类型。一元时间序列的相关研究较多,也逐渐形成一套成熟的理论和方法;然而多元时间序列的数据结构比一元时间序列更复杂,现有的理论和方法仍不够完善。多元时间序列数据在金融、医学、过程监控等领域中被大量采集,因此发展和完善多元时间序列挖掘的方法研究具有重要的意义。
相似性度量是金融时间序列挖掘中的一项关键技术,但现有的度量方法不适合分析小规模的金融多元时间序列。作为金融多元时间序列参数化建模的预处理过程,平稳性分析可以采用聚类方法来完成,但准确率偏低。金融投资组合可以将多个一元时间序列组合成一个多元时间序列,时间序列聚类方法为资产选择提供了有力的支持,但仍缺乏相关的理论和验证。金融高频数据是一种不等间隔的时间序列,现有的相似性查找技术对高频数据的处理效果不佳。
本文以金融多元时间序列相似性分析为研究主线,首先研究了多元时间序列挖掘中的小规模数据相似性度量问题,然后采用时间序列聚类方法来研究平稳性分析和金融投资组合,最后就金融高频数据的相似性查找展开研究。作为研究基础,本文包括了部分一元时间序列挖掘方法的研究。文中也提出了一些解决问题的方法,它们具有一定的理论意义和实际应用价值。本文的主要工作和贡献如下:
1.深入研究金融多元时间序列的数据结构特点,提出采用三维空间的曲面图来描述金融多元时间序列;该方法对其他领域的多元时间序列的形状刻画也具有较好的性能;
2.针对金融领域中的小规模多元时间序列相似性分析,提出了基于点分布特征的多元时间序列相似性度量方法;
3.采用聚类方法实现了金融多元时间序列平稳性的自动分类,并提出了非线性转换理论,大幅度提高了传统平稳性分析方法的准确率;
4.针对金融投资组合问题,提出了多重二值函数的相似性度量方法,并采用时间序列聚类方法建立金融资产选择的依据;
5.提取多元时间序列的自相关函数的多重非线性特征,以此来建立金融高频数据的相似性查找方法,并就金融高频数据的趋势预测展开具体的应用研究。
Time series includes two kinds of data: univariate time series and multivariate time series. There are many researches on univariate time series mining, whose mature theory and methods have been proposed. However, there are a few on multivariate time series mining, since the data structure of multivariate time series is more complex than that of univariate time series. It is of great significance to investigate in multivariate time series mining, because the data of multivariate time series are widely collected from many research and application fields, such as Finance, Monitoring, medicine etc.
Similarity measure is a key technology of time series mining, whose existing methods are not available for the analysis of small-scale multivariate time series. Clustering provides an important support for stationarity analysis, which is the preprocessing of parametric modeling, but the accuracy is still low. It is easy to carry out the transformation from unvaraite time series to multivariate time series with portfolio. though clustering provides a useful way for asset selection, but its ability remains to further investigation. The existing methods of similarity search are not suitable for high frequency financial data, which is a kind of non-interval time series.
The framework of this thesis is based on time series similarity analysis. It first engages in the researches of the similarity analysis for small-scale multivariate time series, and then studies the stationarity analysis and asset selection of portfolio, finally deals with the similarity search of high frequency financial data. Except for some researches on univariate time series as the basic study, this thesis also presents much more important theoretical and practical significance. The majority of our contributions can be summarized as following:
1. The data structure of multivariate time series is deeply studied. Furthermore, the three-dimension curved surface is used to describe the multivariate time series, which is a useful method than can capture the shape character of multivariate time series;
2. A similarity analysis method based on points distribution is presented for small-scale multivariate times series, which can effectively capture the data character of multivariate time series;
3. Clustering method is used to classify time series for stationarity analysis and a nonlinear transformation theory is presented. The combination method is better than the existing methods for stationarity analysis;
4. A new way of asset selection is presented for portfolio, which is based on multiple binary function and time series clustering;
5. The multiple nonlinear trend of autocorrelation function is presented for similarity search of high frequency financial data, and experiments about trend prediction of high frequency financial data have been done.
相似性度量是金融时间序列挖掘中的一项关键技术,但现有的度量方法不适合分析小规模的金融多元时间序列。作为金融多元时间序列参数化建模的预处理过程,平稳性分析可以采用聚类方法来完成,但准确率偏低。金融投资组合可以将多个一元时间序列组合成一个多元时间序列,时间序列聚类方法为资产选择提供了有力的支持,但仍缺乏相关的理论和验证。金融高频数据是一种不等间隔的时间序列,现有的相似性查找技术对高频数据的处理效果不佳。
本文以金融多元时间序列相似性分析为研究主线,首先研究了多元时间序列挖掘中的小规模数据相似性度量问题,然后采用时间序列聚类方法来研究平稳性分析和金融投资组合,最后就金融高频数据的相似性查找展开研究。作为研究基础,本文包括了部分一元时间序列挖掘方法的研究。文中也提出了一些解决问题的方法,它们具有一定的理论意义和实际应用价值。本文的主要工作和贡献如下:
1.深入研究金融多元时间序列的数据结构特点,提出采用三维空间的曲面图来描述金融多元时间序列;该方法对其他领域的多元时间序列的形状刻画也具有较好的性能;
2.针对金融领域中的小规模多元时间序列相似性分析,提出了基于点分布特征的多元时间序列相似性度量方法;
3.采用聚类方法实现了金融多元时间序列平稳性的自动分类,并提出了非线性转换理论,大幅度提高了传统平稳性分析方法的准确率;
4.针对金融投资组合问题,提出了多重二值函数的相似性度量方法,并采用时间序列聚类方法建立金融资产选择的依据;
5.提取多元时间序列的自相关函数的多重非线性特征,以此来建立金融高频数据的相似性查找方法,并就金融高频数据的趋势预测展开具体的应用研究。
Time series includes two kinds of data: univariate time series and multivariate time series. There are many researches on univariate time series mining, whose mature theory and methods have been proposed. However, there are a few on multivariate time series mining, since the data structure of multivariate time series is more complex than that of univariate time series. It is of great significance to investigate in multivariate time series mining, because the data of multivariate time series are widely collected from many research and application fields, such as Finance, Monitoring, medicine etc.
Similarity measure is a key technology of time series mining, whose existing methods are not available for the analysis of small-scale multivariate time series. Clustering provides an important support for stationarity analysis, which is the preprocessing of parametric modeling, but the accuracy is still low. It is easy to carry out the transformation from unvaraite time series to multivariate time series with portfolio. though clustering provides a useful way for asset selection, but its ability remains to further investigation. The existing methods of similarity search are not suitable for high frequency financial data, which is a kind of non-interval time series.
The framework of this thesis is based on time series similarity analysis. It first engages in the researches of the similarity analysis for small-scale multivariate time series, and then studies the stationarity analysis and asset selection of portfolio, finally deals with the similarity search of high frequency financial data. Except for some researches on univariate time series as the basic study, this thesis also presents much more important theoretical and practical significance. The majority of our contributions can be summarized as following:
1. The data structure of multivariate time series is deeply studied. Furthermore, the three-dimension curved surface is used to describe the multivariate time series, which is a useful method than can capture the shape character of multivariate time series;
2. A similarity analysis method based on points distribution is presented for small-scale multivariate times series, which can effectively capture the data character of multivariate time series;
3. Clustering method is used to classify time series for stationarity analysis and a nonlinear transformation theory is presented. The combination method is better than the existing methods for stationarity analysis;
4. A new way of asset selection is presented for portfolio, which is based on multiple binary function and time series clustering;
5. The multiple nonlinear trend of autocorrelation function is presented for similarity search of high frequency financial data, and experiments about trend prediction of high frequency financial data have been done.
引文
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