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.
| Identifer | oai:union.ndltd.org:NSYSU/oai:NSYSU:etd-0825110-194944 |
| Date | 25 August 2010 |
| Creators | Chu, Fang-yu |
| Contributors | Shih-Feng Huang, Mong-Na Lo Huang, Mei-Hui Guo, May-Ru Chen, Fu-Chuen Chang |
| Publisher | NSYSU |
| Source Sets | NSYSU Electronic Thesis and Dissertation Archive |
| Language | English |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0825110-194944 |
| Rights | restricted, Copyright information available at source archive |
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