基于LLSA小波的高频金融时间序列突变点检测研究

发布时间：2018-06-26 20:37

本文选题：小波变换 + 局部线性尺度近似法　；参考：《天津大学》2014年硕士论文

【摘要】：股票价格的变化是由信息的到达所引起的，如何准确及时的掌握新信息的到达，对于揭示股票价格的内在形成机制具有重要的意义，在对股票价格时间序列的分析中，除了长期趋势和季节变动趋势外，还有一种变动也是由外部事件引起并会对时间序列走势产生持续影响，即突变点，包括跳跃点（jumps）、陡坡（steepslopes）等，它往往包含重要信息却被误认为噪声进而被忽视。高频金融时间序列的突变点往往包含重要信息，准确检测和分析突变点的发生对投资决策具有重要意义。统计数据挖掘方法（或模型）需要一种去噪算法来清洗数据，从而获得可靠和显著的结果。大多数数据清洗方法只专注于某些已知类型的不规则行为。对于高频金融数据而言，不规则性是多方面的，，那就是随着不同的时间和不同的测量尺度的变化。因此，找到一个有效的去噪算法是进行高频金融数据挖掘的关键。以往的研究都是在某一尺度上对全体数据使用相同的滤波规则，这存在一个不足：若要保证提取趋势不包含过多噪声则无法包含某些突变现象，相反地，若想检测出突变现象则要付出纳入不必要的干扰噪声的代价。因而本文认为使用小波分析方法研究数据突变点并重构的关键在于是否能准确捕捉突变的同时还保证所提取趋势的相对平滑，也就是说，保证准确检测出突变部分的同时不引入额外的噪声。本文使用一种基于最大重叠离散小波变换（MODWT）的改进型小波分析方法——局部线性尺度近似法（简称LLSA），同时结合线性和非线性滤波器的特点，对高频金融数据进行突变点检测并重构，研究该方法检测出的突变现象能否对应重大特殊事件，以及该方法重构的时间序列是否更贴合实际数据，能否提高预测精度。实证结果表明该方法能有效地检测出突变点的发生，突变点对应了样本期内多件重大经济事件，重构后的时间序列更贴合实际数据，说明LLSA方法在去噪方面的表现优于最大重叠离散小波变换方法，可有效提高预测精度。此外，本文还从多时间尺度的角度检验了此方法的实用性及其经济意义。
[Abstract]:The change of stock price is caused by the arrival of information. How to grasp the arrival of new information accurately and promptly is of great significance to reveal the internal formation mechanism of stock price. In the analysis of the time series of stock price, there is a kind of change also caused by external events in addition to the long-term trend and the trend of seasonal variation. It also has a continuous impact on the trend of time series, namely, the point of mutation, including jumping point (jumps), steep slope (steepslopes) and so on. It often contains important information but is mistaken for noise and is ignored. The mutation points of the high frequency financial time series often contain important information. It is important for the investment decision to detect and analyze the occurrence of the mutation point accurately. Statistical data mining methods (or models) require a denoising algorithm to clean data so as to obtain reliable and significant results. Most data cleaning methods only focus on some known types of irregular behavior. For high frequency financial data, the irregularity is multifaceted, that is, with different time and different measurements. Therefore, finding an effective denoising algorithm is the key to high frequency financial data mining.
Previous studies have used the same filtering rules for all data at a certain scale. There is a shortage: to ensure that the extraction trend does not contain too much noise, some mutation phenomena can not be included. On the contrary, if we want to detect the mutation phenomenon, it is necessary to pay the cost of the unnecessary interference noise. The key of the wavelet analysis method to study the mutation and reconstruction of the data is whether it can capture the mutation accurately and ensure the relative smoothness of the extracted trend, that is to say, it ensures the exact detection of the abrupt part without introducing the extra noise. In this paper, an improved wavelet based on the maximum overlapping discrete wavelet transform (MODWT) is used in this paper. The analysis method, local linear scale approximation (LLSA), combined with the characteristics of linear and nonlinear filters, to detect and reconstruct the catastrophe point of high frequency financial data, and to study whether the mutation can correspond to the major special events and whether the time series rebuilt by the method can be more suitable for the actual data. The results show that the method can detect the occurrence of catastrophe point effectively. The mutation point corresponds to a number of major economic events in the sample period. The reconstructed time series is more close to the actual data, indicating that the performance of the LLSA method in denoising is better than the maximum overlapping and scatter wavelet transform method, which can effectively improve the prediction accuracy. In addition, the practicability and economic significance of this method are examined from the perspective of multiple time scales.
【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】：F832.51

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