傅承德臺灣大學:財務金融學研究所白斯宇Pai, Szu-YuSzu-YuPai2010-05-112018-07-092010-05-112018-07-092008U0001-2406200813552500http://ntur.lib.ntu.edu.tw//handle/246246/182629本篇論文中，我們討論了改變點偵測的問題，傳統上，改變點偵測的問題已有一個廣為人知的方法， the cumulative sum (CUSUM) procedure。然而，在使用 CUSUM 時，我們必須知道時間序列改變前與改變後的機率密度函數，這使得我們在偵測前必須對資料做出很多假設。在此，我們提供一個新的方法可用於改變點偵測，並且不須對資料做出過多假設。新的方法使用到了希爾伯特-黃轉換 (HHT) ，這個新方法(我們稱之為 the HHT test)，不需要對資料做出模型假設，並且，在某些情況下表現的比傳統的 CUSUM 出色。最後，我們並提供一些實證研究作為參考，我們針對次級房貸與網路泡沫化時的 S&P 500 指數做 the HHT test，並且也有不錯的結果。In this paper, we discuss the problems of change point detection. There are some classical methods for change point detection, such as the cumulative sum (CUSUM) procedure. However, when utilizing CUSUM, we must be sure about the model of the data before detecting.e here introduce a new method to detect the change points by using Hilbert-Huang Transformation (HHT) to devise a new algorithm. This new method (called the HHT test in this paper) has the advantage that no model assumptions are required. Moreover, in some cases the HHT test performs better than the CUSUM test, and has better simulation results. In the end, an empirical study of the volatility change based on S&P 500 is also given for illustration.1 Introduction .1 background..........................................1.2 Previous Studies in Change Point Detection .........2.3 Use Hilbert-Huang Transformation on Change Point detection...........................................5.3.1 Hilbert-Huang Transformation........................6.3.2 The process of Hilbert-Huang Transformation.........7 Change Point detection: Volatility Change 10.1 Volatility Change in Normal Distribution Models....10.2 Volatility Change in Geometric Brownian Motion Models.............................................13.3 Volatility Change in Markov Switch Models..........16.4 A Brief Summary....................................19 Change Point detection: The Change of the mean 20.1 The Change of the Mean in Normal Distribution Models.............................................20.2 The Change of the Mean in Brownian Motion Models...22.3 A Brief Summary....................................27 Empirical Study 28.1 Volatility Change Data (Subprime mortgage crisis in 2007)..............................................28.1.1 Using Stock price directly.........................28.1.2 Using Log return of stock price....................32.2 Volatility Change Data (Dot-com bubble in 2000)....36.3 A Brief Summary....................................40 Conclusions and Further Researches 41.1 Conclusions........................................41.2 Further Researches.................................43 References 44application/pdf2314467 bytesapplication/pdfen-US套利偵測改變點偵測希爾伯特-黃轉換波動率股價Arbitrage detectionchange point detectionHilbert-Huang transformationvolatilitystock pricesthesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/182629/1/ntu-97-R95723064-1.pdf