對於各股價指數是否存有結構性之變動及相關性,常用的分析方法有相關係數、單根檢定(如DF Test、 ADF Test)、結構變動檢定(如Chow Test)、自我相關條件異質變異模型(如ARCH模型)、向量自我迴歸模型(VAR模型)或Johansen共整合檢定等。經研究發現,利用多尺度熵(Multiscale Entropy,簡稱MSE)法檢定具有結構性變動之模擬序列時,當序列分割成若干子序列後,存有變動點的子序列其熵值在不同時間尺度下的趨勢會有顯著的差異。本研究嘗試將多尺度熵法應用於分析各別股票市場最具代表性的股價指數資料,如亞洲市場的台灣加權股價指數(TWII)、香港恆生指數(HIS) ;美洲市場的道瓊工業指數(DJI)、那斯達克指數(NASDAQ),以及歐洲市場的英國金融時報指數(FTSE)、法國的CAC40股價指數為主要分析資料,探討各別股票指數是否存有結構性之變動點。實際資料分析發現,所有資料均在2008年9月附近產生結構變化。
The approaches of correlation coefficient, unit root test (such as DF test & ADF test), structural change test (such as Chow test), autoregressive conditional heteroscedasticity (ARCH), vector autoregression model (VAR model) or Johansen cointegration test, etc. are frequently used to test structural changes of stock market indices. However, there are some limitations when using these tools. The literature has found that the multiscale entropy (MSE) can be applied to time series to investigate the issue of change points. Based on this, this paper aimed to apply the multiscale entropy to the stock index of Taiwan Weighted Index (TWII), Hang Seng Index (HSI), Dow Jones Industrial Average Index (DJI), NASDAQ, Financial Times Stock Exchange Index (FTSE) and Cotation Assistée en Continu 40 (CAC40) to test their structural changes and determine the possible time of the change points. From the real data study, we find all of these stock indices have a common structure change point around September of 2008.