Abstract
Widespread use of information and communication technologies has caused that the decisions made in financial markets by investors are influenced by the use of techniques like fundamental analysis and technical analysis, and the methods used are from all branches of mathematical sciences. Recently the fractional Brownian motion has found its way to many applications. In this paper fractional Brownian motion is studied in connection with financial time series. We analyze open, high, low and close prices as a selfsimilar processes that are strongly correlated. We study their basic properties explained in Hurst exponent exponent, and we use them as a measure of predictability of time series.
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References
Bayraktar, E., Poor, H.V., Sicar, K.R.: Efficient estimation of the hurst parameter in high frequency financial data with seasonalities using wavelets. In: Proceedings of 2003 International Conference on Computational Intelligence for Financial Engineering (CIFEr2003), Hong-Kong, 21–25 Mar 2003
Beran, J.: Statistics for Long-memory Processes. Chapman and Hall, New York (1994)
Di Matteo, T., Aste, T., Dacorogna, M.M.: Long-term memories of developed and emerging markets: Using the scaling analysis to characterize their stage of development. J. Bank. Financ. 29, 827–851 (2005). doi:10.1016/j.jbankfin.2004.08.004
Kahane, J.P.: Some Random Series of Functions, 2nd edn. Camridge University Press, London (1985)
Mandelbrot, B.B., Van Ness, J.W.: Fractional Brownian motions, fractional noises and applications. SIAM Rev. 10, 422–437 (1968)
Nualart, D.: Fractional Brownian motion: stochastic calculus and applications, In: Proceedings of the International Congress of Mathematicians, pp. 1541–1562. European Mathematical Society, Madrid, Spain (2006)
Van Ness: Fractional Brownian motion, fractional noises and applications. SIAM Rev. 10, 422–437 (1968)
Qian, H., Raymond, G.M., Bassingthwaighte, J.B.: On two-dimensional fractional Brownian motion and fractional Brownian random field. J. Phys. A: Math. Gen. 31, L527–L535 (1998)
Peters, E.E.: Fractal Market Analysis. Wiley, New York (1994)
Li, D.–Y., Nishimura, Y., Men, M.: Why the long-term auto-correlation has not been eliminated by arbitragers: evidences from NYMEX. Energy Econ. 59, 167–178 (2016). doi:10.1016/j.eneco.2016.08.006
Peters, E.E.: Chaos and Ordered in the Capital Markets. Wiley, New York (1996)
Li, D.–Y., Nishimura, Y., Men, M.: Fractal markets: liquidity and investors on different time horizons. Phys. A 407, 144–151 (2014). doi:10.1016/j.physa.2014.03.073
Power, G.J., Turvey, C.G.: Long-range dependence in the volatility of commodity futures prices: Wavelet-based evidence. Phys. A 389, 79–90 (2010). doi:10.1016/j.physa.2009.08.037
Bohdalová, M., Greguš, M.: Fractal analysis of forward exchange rates. Acta Polytech. Hung. 7(4) 57–69 (2010)
Bohdalová, M., Greguš, M.: Markets, Information and Their Fractal Analysis. E-Leader, New York: CASA, 1–8, (2010)
Investing Ltd.: Crude-oil. http://www.investing.com/commodities/crude-oil-historical-data (n.d.)
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Bohdalová, M., Greguš, M. (2017). Fractional Brownian Motion in OHLC Crude Oil Prices. In: Rojas, I., Pomares, H., Valenzuela, O. (eds) Advances in Time Series Analysis and Forecasting. ITISE 2016. Contributions to Statistics. Springer, Cham. https://doi.org/10.1007/978-3-319-55789-2_6
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DOI: https://doi.org/10.1007/978-3-319-55789-2_6
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