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Long-Range Dependence of Financial Time Series Data

Authors: Chatchai Pesee

Abstract:

This paper examines long-range dependence or longmemory of financial time series on the exchange rate data by the fractional Brownian motion (fBm). The principle of spectral density function in Section 2 is used to find the range of Hurst parameter (H) of the fBm. If 0< H <1/2, then it has a short-range dependence (SRD). It simulates long-memory or long-range dependence (LRD) if 1/2< H <1. The curve of exchange rate data is fBm because of the specific appearance of the Hurst parameter (H). Furthermore, some of the definitions of the fBm, long-range dependence and selfsimilarity are reviewed in Section II as well. Our results indicate that there exists a long-memory or a long-range dependence (LRD) for the exchange rate data in section III. Long-range dependence of the exchange rate data and estimation of the Hurst parameter (H) are discussed in Section IV, while a conclusion is discussed in Section V.

Keywords: Fractional Brownian motion, long-rangedependence, memory, short-range dependence.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1079184

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References:


[1] E. Alos, O. Mazet, and D. Nualart, "Stochastic calculus with respect to fractional Brownian motion with hurst parameter less than ›", Stochastic Processes and their Applications, 2000, vol. 86, pp.121-139.
[2] A. Assaf and J. Cavalcante, "Long range dependence in the returns and volatility of the Brazilian stock market", European Review of Economic and Finance, vol 4, 2005, pp. 1-19.
[3] R.T. Baillie, "Long memory processes and fractional integration in econometrics", Journal of Econometrics, 1996, vol. 73, pp.5-59.
[4] Y.W. Cheung, "Long memory in foreign-exchange rates", Business and Economic Statistics, vol. 11, 1993, pp. 93-101.
[5] F. Comte and E. Renault, "Long memory continuous-time models", Journal of Econometrics, 1996, vol.73, pp.101-149.
[6] F. Comte and E. Renault, "Long memory in continuous time stochastic volatility models", Mathematical Finance, 1998, vol.8, pp.291-323.
[7] W. Dai and C.C. Heyde, "Ito-s formula with respect to fractional Brownian motion and its application", J. Appl. Math. Stoch. Anal., 1996, vol.9, pp.439-448.
[8] L.Decreusefond and A.S. Ustunel, " Fractional brownian motion:theory and applications", Fractional Differential Systems: Models, Methods and Applications, 1998, vol. 5, pp.75-86.
[9] C.W.J. Granger and Z.Ding, "Varieties of long-memory models", Journal of Econometrics, 1996, vol. 73, pp.61-77.
[10] C.W.J. Granger and R.Joyeux, "An introduction to long-memory times series models and fractional differencing", Journal of Time Series Analysis, 1980, vol. 1, no 1, pp.15-29.
[11] C.C. Heyde, "A risky asset model with strong dependence", Journal of Applied Probability, 1999, vol. 36, pp.1234-1239.
[12] C.C. Heyde and S.Liu, "Empirical realities for a minimum description risky asset model. The need for fractal features. Principal invited paper, Mathematics in the New Millenium Conference, Seoul, Korea, October 2000", J. Korean Math. Soc., 2001, vol. 38, pp.1047-1059.
[13] J.R.M. Hosking, " Fractional differencing", Biometrika, 1981,vol. 68, no 1, pp.165-176.
[14] A. Lo, "Long-term memory in the market prices", Econometrica, 1991, vol. 59, pp.1279-1313.
[15] B.B. Mandelbrot and J.W. Van Ness, "Fractional Brownian motions, fractional noises and applications", SIAM Review, 1968, vol.10, no 4, pp.422-437.
[16] I. Norros, E. Valkeila, and J. Virtamo, " An elementary approach to a Girsanov formula and other analytical results on fractional Brownian motion", Bernoulli, 1999, vol. 5, pp.571-587.
[17] W.Willinger, M.S. Taqqu, and V.Teverovsky, " Stock market prices and long- range dependence", Finance and Stochastics, 1999, vol. 3, pp. 1-13.