本文選題：小波變換 + 局部線性尺度近似法　； 參考：《天津大學(xué)》2014年碩士論文

【摘要】：股票價格的變化是由信息的到達所引起的，如何準確及時的掌握新信息的到達，對于揭示股票價格的內(nèi)在形成機制具有重要的意義，在對股票價格時間序列的分析中，除了長期趨勢和季節(jié)變動趨勢外，還有一種變動也是由外部事件引起并會對時間序列走勢產(chǎn)生持續(xù)影響，即突變點，包括跳躍點（jumps）、陡坡（steepslopes）等，它往往包含重要信息卻被誤認為噪聲進而被忽視。高頻金融時間序列的突變點往往包含重要信息，準確檢測和分析突變點的發(fā)生對投資決策具有重要意義。統(tǒng)計數(shù)據(jù)挖掘方法（或模型）需要一種去噪算法來清洗數(shù)據(jù)，從而獲得可靠和顯著的結(jié)果。大多數(shù)數(shù)據(jù)清洗方法只專注于某些已知類型的不規(guī)則行為。對于高頻金融數(shù)據(jù)而言，不規(guī)則性是多方面的，，那就是隨著不同的時間和不同的測量尺度的變化。因此，找到一個有效的去噪算法是進行高頻金融數(shù)據(jù)挖掘的關(guān)鍵。 以往的研究都是在某一尺度上對全體數(shù)據(jù)使用相同的濾波規(guī)則，這存在一個不足：若要保證提取趨勢不包含過多噪聲則無法包含某些突變現(xiàn)象，相反地，若想檢測出突變現(xiàn)象則要付出納入不必要的干擾噪聲的代價。因而本文認為使用小波分析方法研究數(shù)據(jù)突變點并重構(gòu)的關(guān)鍵在于是否能準確捕捉突變的同時還保證所提取趨勢的相對平滑，也就是說，保證準確檢測出突變部分的同時不引入額外的噪聲。本文使用一種基于最大重疊離散小波變換（MODWT）的改進型小波分析方法——局部線性尺度近似法（簡稱LLSA），同時結(jié)合線性和非線性濾波器的特點，對高頻金融數(shù)據(jù)進行突變點檢測并重構(gòu)，研究該方法檢測出的突變現(xiàn)象能否對應(yīng)重大特殊事件，以及該方法重構(gòu)的時間序列是否更貼合實際數(shù)據(jù)，能否提高預(yù)測精度。實證結(jié)果表明該方法能有效地檢測出突變點的發(fā)生，突變點對應(yīng)了樣本期內(nèi)多件重大經(jīng)濟事件，重構(gòu)后的時間序列更貼合實際數(shù)據(jù)，說明LLSA方法在去噪方面的表現(xiàn)優(yōu)于最大重疊離散小波變換方法，可有效提高預(yù)測精度。此外，本文還從多時間尺度的角度檢驗了此方法的實用性及其經(jīng)濟意義。
[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.
【學(xué)位授予單位】：天津大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2014
【分類號】：F832.51

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