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A Study of Longterm Memory in Stock Market Prices Using Rescaled Range Analysis

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Abstract

Most of the studies on the behaviourof the Indian stock market using the autocorrelation function have revealed that the stock market is weakly efficient and the time series of stock prices and stock indices are random walks. The autocorrelation function assumes Gaussian or near-Gaussian properties in the underlying distribution. The distribution function is assumed to have the normal bellshaped curve. Mandelbrot [1972] has proved that the autocorrelation function works well in determining short-term dependence only. But it tends to underestimate long-run correlation for non-Gaussian series. Alternatively the Rescaled Range Analysis is used to study the long-term dépendance in the time series. The Rescaled Range Analysis (R/S Analysis) is a nonparametric methodology developed by H. E. Hurst, a British hydrologist in 1951. Originally this methodology was applied to study the long-term storage capacity of reservoirs and later it was extended to study many natural systems. This statistical methodology is used for distinguishing random time series from biased random time series (Fractal time series) and to study the persistence of trends and also the presence of periodic and nonperiodic cycles in a time series. In this paper a study of the Indian stock market is carried out using the method of Rescaled Range Analysis and Hurst Coefficient. We conclude that the series of stock prices have persistent behaviour. Nearly 18% of the stock prices are influenced by the past. This ‘memory effect’ in the case of stock indices is found to be 23%. The stock market has shown persistent trends and that the series of prices and indices are biased random walks. The present prices are influenced by the past prices and this influence goes across time scales, one period influencing all the subsequent periods.

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Bibliography

  1. Anis, A. A., and Lloyd, E.H., [1976] “The Expected Value of the Adjusted Rescaled Hurst Range of Independent Normal Summands,” Biometrika 63.

  2. Aydogan K, Booth G., [1988] “Are there long cycles in common stock returns?” Southern Economic Journal 55, pp. 141–149.

    Article  Google Scholar 

  3. Bachelier, L., “Theory of Speculation,” in P. Cootner, ed., The Random Character of Stock Market Prices. Cambridge, MA: M.I.T. Press, 1964. (Originally published in 1900.)

    Google Scholar 

  4. Barua S. K., [1981] “The Short-Run Price Behaviour of Securities-Some Evidence on Efficiency of Indian Capital Market”, Vakalp Vol. 6, No. 2.

    Google Scholar 

  5. Ding Z, Granger C, and Engle R.F., [1993] “A Long Memory Property of Stock Market Returns and a New Model.” Journal of Empirical Finance 1, pp. 83–106

    Article  Google Scholar 

  6. Edgar E. Peters., [1989] “Fractal Structure in the Capital Markets,” Financial Analysis Journal, (July-August 1989), pp. 32–37

    Google Scholar 

  7. Edgar. E. Peters., [1994] Fractal Market Analysis-Applying Chaos Theory to Investment and Economics., John Wiley and Sons, New York, 1994.

    Google Scholar 

  8. Edgar. E. Peters., [1997] Chaos and Order in Capital Markets, John Wiley and Sons, New York, 1997.

    Google Scholar 

  9. Fama, Eugene F., [1965] “The Behavior of Stock Market Prices”, Journal of Business, Vol. 38, No. 1, pp. 34–105

    Article  Google Scholar 

  10. Fama, Eugene F., [1970] “Efficient Capital Markets-A Review of Theory and Empirical Work”. The Journal of Finance, Vol. 25, No.2, pp. 383–417

    Article  Google Scholar 

  11. Granger CWJ, and Joyeux R., [1980] “An Introduction to Long-Memory Time Series Models and Fractional Differencing” Journal of Time Series Analysis 1, pp. 15–29

    Article  Google Scholar 

  12. Greene, M., and B. Fielitz [1977] “Long-Term Dependence in Common Stock Returns,” Journal of Financial Economics, 4, pp. 339–349

    Article  Google Scholar 

  13. Gupta O. P., [1978] “Behavior of Share Prices in India”, Doctoral Dissertation, University of Delhi, Delhi.

    Google Scholar 

  14. Hiemstra C, and Jones J.D., [1997] “Another Look at Long Memory in Common Stock Returns” Journal of Empirical Finance 4, pp. 373–401.

    Article  Google Scholar 

  15. Hosking J.R.M., [1981] “Fractional Differencing” Biometrika 68, pp. 165–176

    Article  Google Scholar 

  16. Hurst H. E., [1951] “Long-term Storage of Reservoirs.” Trans. Am. Soc. Civ. Eng. 116, pp. 770–808

    Google Scholar 

  17. Kaen, F.R. and Rosenman R., [1986] “Predictable Behaviour in Financial Markets: Some Evidence in Support of Heiner’s Hypothesis.” American Economic Review 76, pp. 212–220

    Google Scholar 

  18. Krishna Rao N. and Mukherji K., [1971] “Random Walk Hypothesis-An Empirical Study”, Arthaniti, Vol. 14, and No. 1 & 2.

    Google Scholar 

  19. Lee D.K.C. and Robinson P.M., [1996] “Semi-parametric exploration of long memory in stock market prices.” Journal of Statistical Planning and Inference 50, pp. 155–174

    Article  Google Scholar 

  20. Lo Andrew W and MacKinlay AC [1988] “Stock Market Prices do not follow Random Walks: Evidence from a Simple Specification Test.” Review of Financial Studies 1, pp. 41–66

    Article  Google Scholar 

  21. Lo Andrew W. [1991] “Long-Term Memory in Stock Market Prices” Ëconometrica, Vol. 59, No. 5, pp. 1279–1313

    Article  Google Scholar 

  22. Lorie, James H, and Marry E. Hamilton [1973] The Stock Market Theories and Evidence, Homewood Illinois: Richard D. Irwin.

    Google Scholar 

  23. Lux T. [1995] “Herd Behaviour, Bubbles and Crashes.” The Economic Journal 105, 881–896.

    Article  Google Scholar 

  24. Mandelbrot B. [1971] “When Can Price be Arbitraged Efficiently? A Limit to the Validity of the Random Walk and Martingale Models,” Review of Economic Statistics, 53.

    Article  Google Scholar 

  25. Mandelbrot B. [1972] “Statistical Methodology for Non-Periodic Cycles: From the Covariance to R/S Analysis,” Annals of Economic and Social Measurement 1, 1972.

  26. Mills TC. [1993] “Is There Long Memory in UK Stock Returns?” Applied Financial Economics 3, pp. 303–306.

    Article  Google Scholar 

  27. Obaidullah M., [1990] “Stock Market Efficiency: A Statistical Inquiry”, Chartered Financial Analysis, (July-August)

    Google Scholar 

  28. Poterba J.M. and Summers L.H., [1988] “Mean Reversion in Stock Prices, Evidence and Implication.” Journal of Financial Economics 22, pp. 27–59

    Article  Google Scholar 

  29. Ramachandran J., [1988] “Behavior of Stock Market Prices, Information Assimilation and Market Efficiency”, FPM Thesis, IIM.

    Google Scholar 

  30. Rao N.K., [1988] Stock Market Efficiency: The Indian Experience, Anmol Publications, New Delhi.

    Google Scholar 

  31. Robinson P.M [1994] “Efficient Tests of Non-stationary Hypotheses” Journal of the American Statistical Association 89, pp. 1420–1437

    Article  Google Scholar 

  32. Sadique, S and Silvapulle, P [2001] Long-Term Memory in Stock Market Returns: International Evidence” International Journal of Finance and Economics 6, pp. 59–67

    Article  Google Scholar 

  33. Sharma J. L. and Robert E. Kennedy [1977] “A Comparative Analysis of Stock Price Behavior on the Bombay, London and New York Stock Exchanges”, Journal of Financial and Quantitative Analysis. Sept. 1977.

    Google Scholar 

  34. Sharma J. L. [1983] “Efficient Capital Markets and Random Character of Stock Price Behavior in a Developing Economy”, Indian Economic Journal, Vol. 31, No. 2, (Oct-Dec), pp. 53–70

    Google Scholar 

  35. Srinivasan S., Mohapatra. P., and Sahu. K. [1988] “Weak-Form Efficiency in Indian Stock Market: No Excess Returns for Investors”, Modem Management, Vol. V, No. 2.

    Google Scholar 

  36. Subrata Kumar Mitra [2000] “Profitable Trading Opportunity in Indian Stock Market: An Empirical Study with BSE-Sensex”, The ICFAI Journal of Applied Finance, Vol. 6, No. 3, (July), pp. 36–49

    Google Scholar 

  37. Sunil Poshakwale [1996] “Evidence of Weak Form Efficiency and Day of the Week Effect in the Indian Stock Market.” Finance India, Vol. X No. 3, (September), pp. 605–616

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, The American College, Madurai, 625 002, India

    A. Chandra Babu

  2. Dept, of Applied Mathematics and Statistics, M. K. University, Madurai, 625 021, India

    G. Arivarignan (Professor and Head)

  3. Dept, of Commerce, M. K. University, Madurai, 625 021, India

    Punithavathy Pandian (Professor)

Authors
  1. A. Chandra Babu
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  2. G. Arivarignan
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  3. Punithavathy Pandian
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Chandra Babu, A., Arivarignan, G. & Pandian, P. A Study of Longterm Memory in Stock Market Prices Using Rescaled Range Analysis. J. Quant. Econ. 1, 134–146 (2003). https://doi.org/10.1007/BF03404654

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