(54.236.58.220) 您好!臺灣時間:2021/03/08 09:45
字體大小: 字級放大   字級縮小   預設字形  
回查詢結果

詳目顯示:::

我願授權國圖
: 
twitterline
研究生:朱芳玉
研究生(外文):Fang-yu Chu
論文名稱:在自我相似過程中的嵌入分支過程之研究
論文名稱(外文):A Study on the Embedded Branching Process of a Self-similar Process
指導教授:郭美惠郭美惠引用關係
指導教授(外文):Mei-Hui Guo
學位類別:碩士
校院名稱:國立中山大學
系所名稱:應用數學系研究所
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2010
畢業學年度:98
語文別:英文
論文頁數:70
中文關鍵詞:分數差分ARMA分數布朗運動Hurst參數嵌入分支過程自我相似過程
外文關鍵詞:embedded branching processfractional ARIMAfractional Brownian motionHurst parameterself-similar process
相關次數:
  • 被引用被引用:0
  • 點閱點閱:100
  • 評分評分:系統版面圖檔系統版面圖檔系統版面圖檔系統版面圖檔系統版面圖檔
  • 下載下載:0
  • 收藏至我的研究室書目清單書目收藏:0
在本篇論文中,我們探討自我相似性質過程的適合度檢定,考慮兩個著名的自我相似過程:分數布朗運動和分數差分ARMA過程。自我相似過程的赫斯(Hurst)參數由Jones和Shen (2004)所提出的嵌入分支過程方法估計得到。此自我相似性質的適合度檢定是基於皮爾(Pearson)卡方檢定的統計量。我們將檢定統計量的虛無假設分佈以近似尺度調整的卡方分佈修正傳統卡方分佈的第一型誤差偏差問題。而檢定統計量的尺度參數和自由度可以經由迴歸模型得到。模擬結果也顯示我們所提出方法可以有效的改進檢定統計量的有限樣本的顯著水準。最後也進行了高頻財務資料和人類心率資料的實證分析。
In this paper, we focus on the goodness of fit test for self-similar property of two well-known processes: the fractional Brownian motion and the fractional autoregressive integrated moving average process. The Hurst parameter of the self-similar process is estimated by the embedding branching process method proposed by Jones and Shen (2004). The goodness of fit test for self-similarity is based on the Pearson chi-square test statistic. We approximate the null distribution of the test statistic by a scaled chi-square distribution to correct the size bias problem of the conventional chi-square distribution. The scale parameter and degrees of freedom of the test statistic are determined via regression method. Simulations are performed to show the finite sample size and power of the proposed test. Empirical applications are conducted for the high frequency financial data and human heart rate data.
1 Introduction 1
2 Theoretical background 3
2.1 Self-similar processes . . . . . . . . . . . . . . . . . . . . 3
2.1.1 Stationary increments of self-similar process . . . . . . . 3
2.2 Processes with self-similar properties . . . . . . . . . . . . 6
2.2.1 Brownian Motion and Fractional Brownian Motion . . . . . . . 6
2.2.2 Gaussian Fractional ARIMA (FARIMA) . . . . . . . . . . . . . 7
2.3 Simulation of the fractional Brownian motion . . . . . . . . . 8
3 Estimation of the Hurst parameter 11
3.1 Embedded branching process (EBP) . . . . . . . . . . . . . . 11
4 Goodness of fit test for self-similarity 14
4.1 The method of goodness of fit test . . . . . . . . . . . . . . 14
4.2 A modification of the goodness of fit test . . . . . . . . . . 15
5 Simulation study 16
5.1 Modification of the program . . . . . . . . . . . . . . . . . 17
5.2 Standardization . . . . . . . . . . . . . . . . . . . . . . . 17
6 Application 19
6.1 High frequency financial data . . . . . . . . . . . . . . . . 19
6.2 Human heart rate data . . . . . . . . . . . . . . . . . . . . 19
7 Conclusion 20
References 21
Appendix 23
Bates, S. and McLaughlin, S. (1996). An investigation of the implusive nature of Ethernet data using stable distributions. In Proceedings of the 12th UK Performance Engineering Workshop (Edited by J. Hillston and R. Pooley), 17-32.
Bates, S. and McLaughlin, S. (1997). Testing the Gaussian assumption for self-similar teletraffic models. IEEE Signal Processing Workshop on higher-Order Statistics, 21-23.
Beran, J. (1994). Statistics for Long-Memory Processes. Chapman and Hall, New York.
Chiang, P. J. (2006). A Study on the Estimation of the Parameter and Goodness of Fit Test for the Self-similar processes. Master thesis, Department of Applied Mathmatics, National Sun Yat-sen University, Kaohsiung, Taiwan.
Coeurjolly, J.F. (2000). Simulation and identification of the fractional brownian motion: a bibliographical and comparative study. Journal of Statistical Software, 5(7),
1-53. URL http://www.jstatsoft.org/v05/i07.
Davis, R.B. and Harte, D.S. (1987). Tests for Hurst effect, Biometrika, 74, 95-101.
Embrechts, P. and Maejima, M. (2002). Selfsimilar Processes. Princeton Series in Applied Mathematica, Princeton University Press.
Feder, J. (1988). Fractals, Plenum Press, New York.
Guo, C. Y. (2004). Studies in the electrocardiogram monitoring indices. Master thesis, Department of Applied Mathmatics, National Sun Yat-sen University, Kaohsiung, Taiwan.
Hurst, H. E. (1951). Long term storage capacity of reservoirs. Transactions of the American Society of Civil Engineers, 116, 770-799.
Jones, O.D. and Shen, Y. (2004). Estimating the Hurst index of a self-similar process via the crossing tree. IEEE Signal Processing Letters, 11(4), 416-419.
Kolmogorov, A.N. (1941) Local structure of turbulence in fluid for very large Reynolds numbers. Transl. in Turbulence. S.K.Friedlander and L.Topper (eds.) (1961), Interscience Publishers, New York, 151-155.
Leland, W.E., Taqqu, M.S., Willinger, W. and Wilson, D.V. (1994). On the self-similar nature of Ethernet tra±c (extended version). ACM Transactions on Networking, 2, 1-14.
Mandelbrot, B.B. and Wallis, J.R. (1969a) Computer experiments with fractional Gaussian noises. Water Resources Res., 5, 1, 228-267.
Mandelbrot, B.B. and Wallis, J.R. (1969b) Some long -run properities of geophysical records. Water Resources Res., 5, 321-340.
Peng, C.-K., Havlin, S., Simons M, and Goldberger, A.L. (1995). Quantification of scaling exponents and crossover phenomena in nonstationary heartbeat time series. Chaos, 5, 82-87.
Tsay, R. S. (2005). Analysis of financial time series, 2nd Edition. Wiley, Hoboken, New Jersey.
Sakalauskien, G. (2003). The Hurst Phenomenon in Hydrology. Environmental Research, Engineering and Management, 3, 16-20.
Taqqu, M.S., Teverovsky, V., and Willinger, W. (1995). Estimators for long-range dependence: an empirical study. Fractals, 3, 4, 785-788.
Wood, A., Chan, G. (1994). Simulation of stationary Gaussian processes in [0,1]^d, Journal of computational and graphical statistics, 3, 4, 409-432.
QRCODE
 
 
 
 
 
                                                                                                                                                                                                                                                                                                                                                                                                               
第一頁 上一頁 下一頁 最後一頁 top
系統版面圖檔 系統版面圖檔