| dc.contributor.advisor | 謝淑貞 | zh_TW |
| dc.contributor.advisor | Shieh,Shwu-Jane | en_US |
| dc.contributor.author (Authors) | 洪榕壕 | zh_TW |
| dc.contributor.author (Authors) | Hung,Jung-Hao | en_US |
| dc.creator (作者) | 洪榕壕 | zh_TW |
| dc.creator (作者) | Hung,Jung-Hao | en_US |
| dc.date (日期) | 2005 | en_US |
| dc.date.accessioned | 14-Sep-2009 13:28:08 (UTC+8) | - |
| dc.date.available | 14-Sep-2009 13:28:08 (UTC+8) | - |
| dc.date.issued (上傳時間) | 14-Sep-2009 13:28:08 (UTC+8) | - |
| dc.identifier (Other Identifiers) | G0093258041 | en_US |
| dc.identifier.uri (URI) | https://nccur.lib.nccu.edu.tw/handle/140.119/32233 | - |
| dc.description (描述) | 碩士 | zh_TW |
| dc.description (描述) | 國立政治大學 | zh_TW |
| dc.description (描述) | 經濟研究所 | zh_TW |
| dc.description (描述) | 93258041 | zh_TW |
| dc.description (描述) | 94 | zh_TW |
| dc.description.abstract (摘要) | 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。 | zh_TW |
| dc.description.abstract (摘要) | 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. | en_US |
| dc.description.tableofcontents | I. Introduction...........................................................................................................1 II. Methodology..........................................................................................................4 2.1 Fractional Brownian Motion................................................................................4 2.2. Fractal and Multifractal.......................................................................................7 2.2.1 Hausdorff dimension.........................................................................................9 2.2.2 Box dimension................................................................................................10 2.2.3 Information dimension....................................................................................11 2.2.4 Correlation dimension.....................................................................................12 2.2.5 Scaling invariance...........................................................................................13 2.2.6 Multifractal......................................................................................................15 2.2.7 Multifractal Processes.....................................................................................20 2.2.8 Partition Functions..........................................................................................21 2.3 Local Hölder Exponents, Multifractal Spectrum and Generalized Fractal Dimension...................................................................................................................22 2.3.1 Local Hölder Exponents.................................................................................22 2.3.2 The Multifractal Spectrum...........................................................................24 2.3.3 Generalized fractal dimensions......................................................................30 2.4 Multifractal analysis based on Wavelet Transform Modulus Maxima......................................................................................................................31 III. Empirical result analysis...................................................................................37 3.1 The Empirical result analysis of S&P and DJIA..............................................37 IV. Conclusions.......................................................................................................49 | zh_TW |
| dc.language.iso | en_US | - |
| dc.source.uri (資料來源) | http://thesis.lib.nccu.edu.tw/record/#G0093258041 | en_US |
| dc.subject (關鍵詞) | 分數布朗運動 | zh_TW |
| dc.subject (關鍵詞) | 自我相似 | zh_TW |
| dc.subject (關鍵詞) | 維度 | zh_TW |
| dc.subject (關鍵詞) | 多重碎形 | zh_TW |
| dc.subject (關鍵詞) | 小波轉換模數最大植 | zh_TW |
| dc.subject (關鍵詞) | Fractional Brownian Motion | en_US |
| dc.subject (關鍵詞) | Multifractal | en_US |
| dc.subject (關鍵詞) | Hausdorff dimemsion | en_US |
| dc.subject (關鍵詞) | Local Hölder exponent | en_US |
| dc.subject (關鍵詞) | Wavelet transform modulus maxima | en_US |
| dc.title (題名) | Multifractal Analysis for the Stock Index Futures Returns with Wavelet Transform Modulus Maxima | zh_TW |
| dc.title (題名) | 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 | zh_TW |
| dc.type (資料類型) | thesis | en |
| dc.relation.reference (參考文獻) | Arneodo, A., Grasseau, G., and Holschneider, M., “Wavelet Transform of Multifractals,” Physical Review Letters, v61, # 20, November (1988), 2281-2284. | zh_TW |
| dc.relation.reference (參考文獻) | Arneodo, A., Barry, E., J. Delour., Muzy, J. F., The thermodynamics of fractals revisited with wavelets, Physica A, 213, 232-275 (1995). | zh_TW |
| dc.relation.reference (參考文獻) | Arneodo, A., Bacry, E., Muzy, J. F.,“Random cascades on wavelet dyadic trees,”Journal of Mathematical Physics, v39, # 8, August (1998), 4142-4164. | zh_TW |
| dc.relation.reference (參考文獻) | Audit, B., Barry, E., Muzy, J. F., Arneodo, A., (2002), Wavelet based estimator of scaling behavior, IEEE. in Information Theory 48, 11, pp 2938-2954. | zh_TW |
| dc.relation.reference (參考文獻) | Barry, E., J. Delour., Muzy, J. F., Modelling financial time series using multifractal random walks., Physica A, 299, 84-92 (2001). | zh_TW |
| dc.relation.reference (參考文獻) | Baillie, R. T., “Long Memory Processes and Fractional Integration in Econometrics,” Journal of Econometrics 73:1 (1996), 5–59. | zh_TW |
| dc.relation.reference (參考文獻) | Baillie, R. T., T. Bollerslev, and H. O. Mikkelsen, “Fractionally Integrated Generalized Autoregressive Conditional Heteroskedasticity,” Journal of Econometrics 74:1 (1996), 3–30. | zh_TW |
| dc.relation.reference (參考文獻) | Baillie, R. T., C. F. Chung, and M. A. Tieslau, “Analyzing Inflation by the Fractionally Integrated ARFIMA-GARCH Model,” Journal of Applied Econometrics 11:1 (1996), 23–40. | zh_TW |
| dc.relation.reference (參考文獻) | Billingsley, P., Probability and Measure, (New York: John Wiley and Sons, 1995). | zh_TW |
| dc.relation.reference (參考文獻) | Billingsley, P., Convergence of Probability Measures, (New York: John Wiley and Sons, 1999). | zh_TW |
| dc.relation.reference (參考文獻) | Bollerslev, T., “Generalized Autoregressive Conditional Heteroskedasticity,” Journal of Econometrics 31:3 (1986), 307–327. | zh_TW |
| dc.relation.reference (參考文獻) | Breidt, F.J., Crato, N. and P. de Lima, 1998, The detection and estimation of long | zh_TW |
| dc.relation.reference (參考文獻) | memory in stochastic volatility, Journal of Econometrics, 83, pp.325-348. | zh_TW |
| dc.relation.reference (參考文獻) | Calvet, L., A. Fisher, and B. B. Mandelbrot, “Large Deviation Theory and the Distribution of Price Changes,” Cowles Foundation discussion paper no. 1165, Yale University, available from the SSRN database at http://www.ssrn.com (1997). | zh_TW |
| dc.relation.reference (參考文獻) | Calvet, L., and A. Fisher, “Forecasting Multifractal Volatility,” Journal of Econometrics 105:1 (2001), 27–58. | zh_TW |
| dc.relation.reference (參考文獻) | Calvet, L., and A. Fisher, “Multifractality in Asset Returns: Theory and Evidence,” Review of Economics and Statistics 84 (2002), 381--406. | zh_TW |
| dc.relation.reference (參考文獻) | Calvet, L., and A. Fisher,“How to Forecast Long-Run Volatility: Regime Switching and the Estimation of Multifractal Processes,” Journal of Financial Econometrics, 2 (2004), 49--83 | zh_TW |
| dc.relation.reference (參考文獻) | Campbell, J., A. Lo, and A. C. MacKinlay, The Econometrics of Financial Markets (Princeton: Princeton University Press, 1997). | zh_TW |
| dc.relation.reference (參考文獻) | Engle, R. F., “Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom In ation,” Econometrica 50:4 (1982), 987–1007. | zh_TW |
| dc.relation.reference (參考文獻) | Engle, R.F. and T. Bollerslev, 1986, Modeling the persistence of conditional | zh_TW |
| dc.relation.reference (參考文獻) | variance, Econometric Reviews, 5, pp.1-50. | zh_TW |
| dc.relation.reference (參考文獻) | Falconer, K. Fractal Geometry: Mathematical Foundations and Applications, (New | zh_TW |
| dc.relation.reference (參考文獻) | York: John Wiley and Sons, 1990) | zh_TW |
| dc.relation.reference (參考文獻) | Fisher, A., L. Calvet, and B. B. Mandelbrot, “Multifractality of Deutsche Mark/US Dollar Exchange Rates,” Cowles Foundation discussion paper no. 1166, Yale University, available from the SSRN database at http://www.ssrn.com (1997). | zh_TW |
| dc.relation.reference (參考文獻) | Goldberger AL, Amaral LAN, Glass L, Hausdorff JM, Ivanov PCh, Mark RG, Mietus JE, Moody GB, Peng C-K, Stanley HE. PhysioBank, PhysioToolkit, and PhysioNet: Components of a New Research Resource for Complex Physiologic Signals. Circulation101(23):e215-e220[CirculationElectronicPages;http://circ.ahajournals.org/cgi/content/full/101/23/e215]; 2000 (June 13). | zh_TW |
| dc.relation.reference (參考文獻) | Lo, A. W., “Long Memory in Stock Market Prices,” Econometrica 59:5 (1991), 1279–1313. | zh_TW |
| dc.relation.reference (參考文獻) | Mandelbrot, B. B., A. Fisher, and L. Calvet, “The Multifractal Model of Asset Returns,” Cowles Foundation discussion paper no. 1164, Yale University, paper available from the SSRN database at http://www.ssrn.com (1997). | zh_TW |
| dc.relation.reference (參考文獻) | Mandelbrot, B. B., and J. W. van Ness, “Fractional Brownian Motion, Fractional Noises and Application, ” SIAM Review 10:4 (1968), 422–437. | zh_TW |
| dc.relation.reference (參考文獻) | Mandelbrot, B.B, Fractals and Scaling in Finance: Discontinuity, Concetration, Risk. Springer, New York (1997). | zh_TW |
| dc.relation.reference (參考文獻) | Muzy, J. F., Bacry, E. and A. Arneodo, Wavelets and Multifractal Formalism for Singular Signals: Application to Turbulence Data, Physical Review Letters, v. 67, # 25, December (1991), pp. 3515-3518. | zh_TW |
| dc.relation.reference (參考文獻) | Muzy, J.F., Bacry ,E. and A. Arneodo,Multifractal formalism for fractal signals. The structure-function approach versus the wavelet-transform modulus-maxima method, Phys. Rev. E 47, 875 (1993). | zh_TW |
| dc.relation.reference (參考文獻) | X. S., Huiping C., Ziqin W., Yongzhuang Yuan, Multifractal analysis of Hang Seng index inHong Kong stockmark et, Phys. A 291 (2001) 553–562. | zh_TW |
| dc.relation.reference (參考文獻) | X. S., Huiping C.,Yongzhuang Y., Ziqin W., Predictability of multifractal analysis of Hang Seng stockindex in Hong Kong, Phys. A 301 (2001) 473–482. | zh_TW |
| dc.relation.reference (參考文獻) | Yu W., Dengshi H., Multifractal analysis of SSEC in Chinese stock market: A different empirical result from Heng Seng index, Phys. A 355 (2005) 497-508. | zh_TW |
