A Study on the Estimation of the Parameter and Goodness of Fit Test for the Self-similar Process

• Main Authors: Pei-Jung Chiang, 蔣佩蓉
• Other Authors: Mong-Na Lo Huang
• Format: Others
• Language: en_US
• Published: 2006
• Online Access: http://ndltd.ncl.edu.tw/handle/79786662122621075793

碩士 === 國立中山大學 === 應用數學系研究所 === 94 === Recently there have been reports that certain physiological data seem to have the properties of long-range correlation and self-similarity. These two properties can be characterized by a long-range dependent parameter d, as well as a self-similar parameter H. In Peng et al (1995), the alteration of long-range correlations with life-threatening pathologies are studied by analyzing the heart rate data of different groups of subjects. The self-similarity properties of two well-known processes, namely the Fractional Brownian Motion (FBM) and the Fractional ARIMA (FARIMA), are of interest to see if it is suitable to be used to model the heart rate data in order to examine the health conditions of some patients. The Embedded Branching Process (EBP) method for estimating parameter $H$ and a goodness of fit test for examining the self-similarity of a process based on the EBP method are proposed in Jones and Shen (2004). In this work, the performance of the goodness of fit test are examined using simulated data from the FBM and FARIMA processes. A modification of the distribution of the test statistics under null hypothesis is proposed and has been modified to be more appropriate. Some simulation comparisons of different estimation methods of the parameter $H$ for some FARIMA processes are also presented and applied to heart rate data obtained from Kaohsiung Veterans General Hospital.