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COMPLEX PATTERNS IN FINANCIAL TIME SERIES THROUGH HIGUCHI’S FRACTAL DIMENSION

T. G. GRACE ELIZABETH RANI

Research and Development Center, Bharathiar University, Coimbatore 641046, Tamil Nadu, India

E-mail Address: fateligna18@gmail.com

Corresponding author.

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and

G. JAYALALITHA

Department of Mathematics, Vel’s University, Pallavaram 600117, Tamil Nadu, India

E-mail Address: ragaji94@yahoo.com

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https://doi.org/10.1142/S0218348X16500481Cited by:4 (Source: Crossref)

Abstract

This paper analyzes the complexity of stock exchanges through fractal theory. Closing price indices of four stock exchanges with different industry sectors are selected. Degree of complexity is assessed through Higuchi’s fractal dimension. Various window sizes are considered in evaluating the fractal dimension. It is inferred that the data considered as a whole represents random walk for all the four indices. Analysis of financial data through windowing procedure exhibits multi-fractality. Attempts to apply moving averages to reduce noise in the data revealed lower estimates of fractal dimension, which was verified using fractional Brownian motion. A change in the normalization factor in Higuchi’s algorithm did improve the results. It is quintessential to focus on rural development to realize a standard and steady growth of economy. Tools must be devised to settle the issues in this regard. Micro level institutions are necessary for the economic growth of a country like India, which would induce a sporadic development in the present global economical scenario.

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References

1. B. B. Mandelbrot, The Fractal Geometry of Nature (W. H. Freeman and Co., New York, 1982). Google Scholar
2. S. Taylor, Modeling Financial Time Series (John Wiley and Sons). Google Scholar
3. E. E. Peters, Chaos and Order in the Capital Markets: A New View of Cycles Prices and Market Volatility, 2nd edn. (John Wiley and Sons Inc., 1996). Google Scholar
4. B. B. Mandelbrot, Fractals and Scaling in Finance (Springer, New York, 1997). Crossref, Google Scholar
5. D. O. Cajueiro, P. Gojas and B. M. Tabak, Does financial market liberalization increase the degree of market efficiency? The case of Athens Stock exchange, Int. Rev. Financ. Anal. 18 (2009) 50–57. Crossref, Google Scholar
6. D. O. Cajueiro and B. M. Tabak, Multi-fractality and herding behavior in the Japanese Stock Market, Chaos Solitons Fractals 40(1) (2009) 497–504. Crossref, Web of Science, Google Scholar
7. Y. Wang, C. Wu and Z. Pan, Multi-fractal de-trending moving average analysis on the US dollar exchange rates, Physica A 390(20) (2011) 3512–3523. Crossref, Web of Science, Google Scholar
8. M. Paulch and L. Jackowska-Strumillo, The influence of using fractal analysis in hybrid MLP model for short-term forecast of close prices of Warsaw Stock Exchange, Proc. 2014 Federated Conf. Computer Science and Information Systems (IEEE), pp. 111–118. Google Scholar
9. P. Paramanathan and R. Uthayakumar, Application of fractal theory in analysis of electroencephalographic signals, Comput. Biol. Med. 38(3) (2008) 372–378. Crossref, Web of Science, Google Scholar
10. T. Bojic, A. Vackovic and A. Kalauzi, Modeling EEG fractal dimension changes in wake and drowsy states in humans — A preliminary study, J. Theor. Biol. 262(2) (2010) 214–222. Crossref, Web of Science, Google Scholar
11. M. Bachmann, A. Suhhova, J. Lass and H. Hinrikus, Revealing small hidden changes in human EEG by Higuchi’s fractal dimension, IFMBE Proc. 38 (2013) 47–50. Crossref, Google Scholar
12. K. J. Falconer, Fractal Geometry: Mathematical Foundations and Applications (John Wiley and Sons, 1990). Google Scholar
13. P. M. Iannaccone and M. K. Khokha, Fractal Geometry in Biological Systems — An Analytical Approach (CRC Press, 1996). Google Scholar
14. T. Higuchi, Approach to an irregular time series on the basis of fractal theory, Physica D 31 (1988) 277–283. Crossref, Web of Science, Google Scholar
15. P. B. Patel and T. Marwala, Forecasting closing price indices using neural networks. IEEE Conf. System, Management and Cybernetics (2006), pp. 2351–2356. Google Scholar