基于小波分析的金融波动模式识别及异常值检测

发布时间：2018-01-15 22:22

本文关键词：基于小波分析的金融波动模式识别及异常值检测　出处：《天津大学》2014年硕士论文　论文类型：学位论文

【摘要】：金融的波动性是所有金融市场的内在特征，其对资产组合配置、金融产品定价、金融风险管理等都有很重要的作用，特别是金融波动模式的识别及相关异常的研究对于市场投资者和监管者来说意义重大。在实际中，主要通过金融资产收益率序列来得出金融波动的特征。本文主要利用将小波分析与符号时间序列分析、D-Markov模型以及金融波动计量模型相结合的方法来研究金融波动序列的模式识别问题和金融收益序列的异常检测问题。本文首先将小波分析、主要应用于工程领域的隐含模式快速识别方法D-Markov模型及符号时间序列分析相结合，引入波动向量之间异常度的概念，提出了一种全新的用于金融波动模式识别及异常模式检测的方法。第一步对金融波动序列进行离散小波变换产生小波系数序列，选择符号集大小，将小波系数序列符号化，并对符号序列进行D-Markov模型分析，计算状态概率向量，得到波动向量的异常度，进而进行模式识别及异常模式的检测。其次基于波动模型对金融收益时间序列的刻画而产生的残差序列，提出了一种以小波分析为基础的异常检测与定位的方法。采用蒙特卡洛模拟选定阈值，分析残差序列离散小波变换后的小波系数序列，标记大于阈值且是最大的小波系数值位置，通过将该位置的值设置为零重建小波系数序列，并通过逆离散小波变换重构残差序列，如此循环，直到小波系数序列满足阈值要求，形成位置集合。进而基于该位置集合来检测和定位异常值。针对本文提出的方法，均以上证综指和深证成指检验了所提方法的可行性和有效性。实证结果表明在选定标准波动模式的情况下，该方法可以实现寻找到类似与标准波动模式的波动时间段；在选定正常波动模式的情况下，可以实现对异常波动模式的检测。而在基于小波分析的异常检测定位时，，可以有效地检测到对数日收益率序列的异常值并且能够准确地对异常值进行定位。
[Abstract]:Financial volatility is the inherent feature of all financial markets, which plays an important role in portfolio allocation, pricing of financial products, financial risk management and so on. In particular, the identification of financial volatility patterns and the study of related anomalies are of great significance to market investors and regulators. This paper mainly uses wavelet analysis and symbolic time series analysis. D-Markov model and financial volatility econometric model are combined to study the pattern recognition problem of financial volatility series and the anomaly detection problem of financial return series. In this paper, firstly, wavelet analysis is combined with D-Markov model and symbolic time series analysis, which is mainly applied in engineering field. The concept of anomaly degree between wave vectors is introduced. A new method for financial volatility pattern recognition and abnormal pattern detection is proposed. In the first step, discrete wavelet transform (DWT) is used to generate the wavelet coefficient sequence and the symbol set size is selected. The wavelet coefficient sequence is symbolized and the D-Markov model is used to analyze the symbol sequence. The state probability vector is calculated and the anomaly degree of the fluctuation vector is obtained. Then the pattern recognition and abnormal pattern detection. Secondly, based on the volatility model to describe the time series of financial returns, the residuals are generated. A method of anomaly detection and localization based on wavelet analysis is proposed. Monte Carlo simulation is used to select the threshold value to analyze the wavelet coefficient sequence of discrete wavelet transform of residual sequence. The mark is larger than the threshold value and is the largest wavelet coefficient value position, by setting the value of the position to zero reconstruction wavelet coefficient sequence, and inverse discrete wavelet transform reconstruction residual sequence, such a cycle. Until the wavelet coefficient sequence meets the threshold requirement, the location set is formed, and then the outlier value is detected and located based on the position set. For the methods proposed in this paper, the Shanghai Composite Index and Shenzhen Composite Index are used to test the feasibility and effectiveness of the proposed method. The empirical results show that in the case of the selection of standard volatility model. This method can find the fluctuation time period similar to the standard fluctuation mode. In the case of selecting normal fluctuation mode, the detection of abnormal fluctuation mode can be realized, but in the case of abnormal detection and localization based on wavelet analysis. The outliers of the daily return series can be detected effectively and the outliers can be accurately located.
【学位授予单位】：天津大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：F830.9

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