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 Title: Multifractal Analysis for the Stock Index Futures Returns with Wavelet Transform Modulus Maxima股價指數期貨報酬率的多重碎形分析與小波轉換的模數最大值 Authors: 洪榕壕Hung,Jung-Hao Contributors: 謝淑貞Shieh,Shwu-Jane洪榕壕Hung,Jung-Hao Keywords: 分數布朗運動自我相似維度多重碎形小波轉換模數最大植Fractional Brownian MotionMultifractalHausdorff dimemsionLocal Hölder exponentWavelet transform modulus maxima Date: 2005 Issue Date: 2009-09-14 13:28:08 (UTC+8) Abstract: 本文應用資產報酬率的多重碎形模型，該模型為一整合財務時間序列上的厚尾及波動持續性的連續時間過程。多重碎形的方法允許我們估計隨時間變動的報酬率高階動差，進而推論財務時間序列的產生機制。我們利用小波轉換的模數最大值計算多重碎形譜，透過譜分解得到資產報率分配的高階動差資訊。根據實證結果，我們得到S&P和DJIA的股價指數期貨報酬率符合動差尺度行為且資料也展現幕律的形態。根據估計出的譜形態為對數常態分配。實證結果也顯示S&P和DJIA的股價指數期貨報酬率均具有長記憶及多重碎形的特性。　　We apply the multifractal model of asset returns (MMAR), a class of continuous-time processes that incorporate the thick tails and volatility persistence of financial time series. 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