外匯市場之長期記憶性探討-以Hurst指數分析

Abstract

金融市場是否為一個效率市場，在近幾十年來，不斷的有學者發展了不同的模型來探討其效率性。Hurst(1951)發展了R/S分析法，此法最初是運用於分析洪水和乾旱的程度，隨後Mandelbrot將此方法運用在金融市場的分析，其對於碎形理論的貢獻甚大，而有「碎形之父」之稱。 本研究將利用R/S分析法，分析從2001年1月1日到2011年12月31日的歐元、日圓、英鎊、澳幣、瑞士法郎、加拿大幣、港幣、瑞典克朗、紐西蘭元、韓元、新加坡元及新台幣等12個貨幣兌美元的匯率，利用此長達12年的日匯率資料先取其日報酬率，再將觀測期間分成3年期、6年期及12年期，來探討外匯的長期記憶性，可得以下幾點結論： 1.將此12個外匯的報酬率，進行Kolmogorov-Smirnov檢定及觀察其峰態係數，結果發所有外匯皆拒絕常態分配的假設，且外匯報酬率皆呈現高狹峰的形態，與過去文獻所探討的報酬率具有厚尾分配之現象相符。 2.外匯報酬率無論是3年期、6年期及12年期，大部份的Hurst指數顯著不等於0.5，表示外匯市場為一種碎形市場，今日的價格將對未來的價格有某程度的影響，效率市場的論點在此並不成立。 3.利用Mann-Whitney U來檢定歐美區域與非歐美區域的外匯報酬率，其Hurst指數與循環週期天數之檢定結果皆不拒絕虛無假設，意謂此兩個區域的Hurst指數與循環週期天數，並不會因為區域的差異而有不同。

Scholars have developed numerous models to investigate the efficiency of financial market for several years. Hurst(1951) developed Rescaled Range Analysis (R/S analysis), and was initially used to analyze flood and drought. Mandelbrot applied R/S Analysis on financial market, and his contribution made him called the Father of Fractal. This research analyzes the exchange rate of 12 currrencies to USD from 2001.1.1 to 2011.12.31 by R/S Analysis. By observing daily rate of return in 12 years and seperated observation period into 3 years, 6 years and 12 years, to discuss long memory in Foreign Exchange Market. The results are as follows: 1. Using Kolmogorov-Smirnov Test to observe the kurtosis of the rate of return (12 currencies), and found all currencies reject normal distribution hypothesis; furthermore, leptokurtosis was found in all the exchange rate of return, which fit past experience. 2. The Hurst Index of all the exchange rate of return in each period (3 years, 6 years and 12 years) are significant. 3. Index equal to 0.5 means foreign exchange market is a fractal market, there are some relations between markets in different time, hypothesis of efficiency market can't be established. 4. Testing Euro and American area to non-Euro and non-American area's exchange rate of return by Mann-Whitney U, and figures out that both Hurst Index and non-periodic cycle test are not reject null hypothesis, which means Hurst Index and non-periodic cycle don't vary because different areas.