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Abstract

In this article, the traditional rescaled range analysis (R/S) is used to distinguish a random series from a fractal series. It is used to determine the persistence in trends of the financial time and to detect the long-memory effect of these financial time series over a long period of time. All chaotic systems have a quantifying measurement known as a fractal dimension. The Fractal Dimension Index (FDI) is a specialised tool that applies the principles of chaos theory and fractals. With FDI one can determine the persistence or anti-persistence of any equity or commodity. In this article, the FDI is computed from the Hurst exponent, and the Hurst exponent is computed from rescaled range (R/S). Data from Indian Mutual Funds and Indian Stock Markets are analysed using these statistical techniques and graphs are plotted for finding the most persistent of the financial series and the long-term memory content of these series are also analysed.

Keywords

Time-series persistent rescaled range analysis fractal Dimension Index

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References

Granger

C.W.J.

Joyeux

(1980). An introduction to long memory time series models and fractional differencing. Journal of Time Series Analysis, 1(1), 15–29.

Greene

M.T.

Fielitz

B.D.

(1977). Long-term dependence in common stock returns. Journal of Financial Economics, 4(3), 339–349.

Hosking

J.R.M.

(1981). Fractional differencing. Biometrika, 68(1), 165–176.

Hurst

H.E.

(1951). Long-term storage capacity of reservoirs. Transactions of the American Society of Civil Engineers, 116, 770–808.

Mandelbrot

(1972). Statistical methodology for non-periodic cycles from the co-variances of R/S Analysis. Annals of Economics and Social Measurement, 1(3), 189–196.

Mandelbrot

Wallis

(1968). Noah, Joseph and operational hydrology. Water Resources Research, 4(5), 909–918.

Mandelbrot

Taqqu

(1979). Robust R/S analysis of long-run serial correlation. Bulletin of the International Statistical Institute, 48(2), 59–104.

Peters

Edgar. E.

(1989). Fractal structure in the capital markets. Financial Analysts Journal, 45(4), 32–37.

Peters

Edgar. E.

(1991). Chaos and order in capital markets. New York: John Wiley and Sons.

10.

Peters

Edgar. E.

(1994). Fractal market analysis. New York: John Wiley and Sons.

Fractal Analysis of Indian Financial Markets: An Empirical Approach

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