Title page for etd-0825110-194944


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URN etd-0825110-194944
Author Fang-yu Chu
Author's Email Address No Public.
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Department Applied Mathematics
Year 2009
Semester 2
Degree Master
Type of Document
Language English
Title A Study on the Embedded Branching Process of a Self-similar Process
Date of Defense 2010-06-25
Page Count 70
Keyword
  • embedded branching process
  • fractional ARIMA
  • fractional Brownian motion
  • Hurst parameter
  • self-similar process
  • Abstract 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.
    Advisory Committee
  • Mong-Na Lo Huang - chair
  • Fu-Chuen Chang - co-chair
  • May-Ru Chen - co-chair
  • Shih-Feng Huang - co-chair
  • Mei-Hui Guo - advisor
  • Files
  • etd-0825110-194944.pdf
  • indicate in-campus access only
    Date of Submission 2010-08-25

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