Please use this identifier to cite or link to this item: https://ah.nccu.edu.tw/handle/140.119/32233


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 Motion
Multifractal
Hausdorff dimemsion
Local Hölder exponent
Wavelet 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. The multifractal approach allows for higher moments of returns that may vary with the time horizon and leads to infer about the generating mechanism of the financial time series. The multifractal spectrum is calculated by the Wavelet Transform Modulus Maxima (WTMM) provides information on the higher moments of the distribution of asset returns and the multiplicative cascade of volatilities. We obtain the evidences of multifractality in the moment-scaling behavior of S&P and DJIA stock index futures returns and the moments of the data represent a power law. According to the shape of the estimated spectrum we infer a log normal distribution.The empirical evidences show that both of them have long memory and multifractal property.
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Description: 碩士
國立政治大學
經濟研究所
93258041
94
Source URI: http://thesis.lib.nccu.edu.tw/record/#G0093258041
Data Type: thesis
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