{"title":"Long-Range Dependence of Financial Time Series Data","authors":"Chatchai Pesee","country":null,"institution":"","volume":20,"journal":"International Journal of Mathematical and Computational Sciences","pagesStart":518,"pagesEnd":523,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/12428","abstract":"This paper examines long-range dependence or longmemory\r\nof financial time series on the exchange rate data by the\r\nfractional Brownian motion (fBm). The principle of spectral density\r\nfunction in Section 2 is used to find the range of Hurst parameter (H)\r\nof the fBm. If 0< H <1\/2, then it has a short-range dependence\r\n(SRD). It simulates long-memory or long-range dependence (LRD) if\r\n1\/2< H <1. The curve of exchange rate data is fBm because of the\r\nspecific appearance of the Hurst parameter (H). Furthermore, some\r\nof the definitions of the fBm, long-range dependence and selfsimilarity\r\nare reviewed in Section II as well. Our results indicate that\r\nthere exists a long-memory or a long-range dependence (LRD) for\r\nthe exchange rate data in section III. Long-range dependence of the\r\nexchange rate data and estimation of the Hurst parameter (H) are\r\ndiscussed in Section IV, while a conclusion is discussed in Section V.","references":null,"publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 20, 2008"}