- 學位論文
財務時間數列的長期指數相關性偵測：以台股上市公司為例
Detecting Long-range Power-law Correlations in Financial Time Series: A Case on Listed Companies of Taiwan Stock Market
摘要
在時間數列分析中，有許多的分析方法被應用在各個不同的領域，有些分析方法還可被用在長記憶分析上。有一個新的分析方法，稱之為解趨勢波動分析法（Detrended Fluctuation Analysis：DFA），它原本是用來對DNA序列中偵測長期指數相關性。在這篇論文中，我們利用DFA法對台灣股市中的三種類型資料（主要股價指數，類股指數，以及個股指數），做長期指數相關性偵測。最後實驗結果指出，在台灣股市中，主要股價指數、類股指數與個股指數存在著長期記憶性。另外我們也發現，主要股價指數所偵測出的相關性並不代表所有的類股指數與個股指數所偵測出的相關性會與其相同，但也發現超過一半以上的類股指數與個股指數所偵測出的相關性與主要股價指數相同。
關鍵字
時間數列分析並列摘要
In time series analysis, there have been many statistic models widely used; some models could estimate long memory. A new idea for analyzing time series is Detrended Fluctuation Analysis (DFA), which was originally developed for finding long-rage power-law correlations in DNA sequences. We apply DFA to Taiwan stock market for three categories of data: TAIEX (Taiwan Stock Exchange Capitalization Weighted Stock Index), the group indices aggregated from individual stock indices, and individual stock indices. The results show that long memory exists in most listed companies of Taiwan stock market for the cases when scaling exponent not equals to 0.5. However, the correlations detected from aggregated data series do not imply the correlation of original data series. Our findings are that the correlations detected from main index do not imply the same correlation of group indices and individual stock indices, but there are greater than half of group indices and individual stock indices following the same correlation with the main index.