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Stock Price Modeling: Separation of Trend and Fluctuations, and Implications

Author

Listed:
  • B. D. Craven

    (Department of Mathematics & Statistics, University of Melbourne, Victoria 3010, Australia)

  • Sardar M. N. Islam

    (VISES, Victoria University, Melbourne, Victoria 8001, Australia)

Abstract

A series of stock prices typically shows a large trend and smaller fluctuations. These two parts are often studied together, as if parts of a single process; but they appear to be separately caused. In this paper, the two parts are analyzed separately, so that one does not distort the other, and some spurious interaction terms are avoided. This contributes a model, in which a wide range of features of stock price behavior are identified. With logarithms of stock prices, the two parts become of more comparable size. This is found to lead to a simpler additive model. On a logarithmic scale, the stock prices show the trend as a straight line (which can be extrapolated), with added fluctuations filling a narrow band. The trend and fluctuations are thus separated. The trend appears to be largely generated by a positive feedback process, describing investor behavior. The width of the fluctuation band does not grow with time, so positive feedback is not its cause. The movement of stock prices can be understood by analyzing the trend and fluctuations as separate processes; the latter considered as a stationary stochastic process with a scale factor. This analysis is applied to a historical dataset (S&P500 index of daily prices from February 1928). Here, the fluctuations are autocorrelated over short time intervals; there is little structure, except for market crash periods, when variability increases. The slope of the trend showed some jumps, not predictable from price history. This approach to modeling describes many aspects of stock price behavior, which are usually discussed in behavioral finance.

Suggested Citation

  • B. D. Craven & Sardar M. N. Islam, 2015. "Stock Price Modeling: Separation of Trend and Fluctuations, and Implications," Review of Pacific Basin Financial Markets and Policies (RPBFMP), World Scientific Publishing Co. Pte. Ltd., vol. 18(04), pages 1-12, December.
  • Handle: RePEc:wsi:rpbfmp:v:18:y:2015:i:04:n:s0219091515500277
    DOI: 10.1142/S0219091515500277
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    References listed on IDEAS

    as
    1. B. Craven & Sardar Islam, 2008. "A model for stock market returns: non-Gaussian fluctuations and financial factors," Review of Quantitative Finance and Accounting, Springer, vol. 30(4), pages 355-370, May.
    2. Yanhui Liu & Parameswaran Gopikrishnan & Pierre Cizeau & Martin Meyer & Chung-Kang Peng & H. Eugene Stanley, 1999. "The statistical properties of the volatility of price fluctuations," Papers cond-mat/9903369, arXiv.org, revised Mar 1999.
    3. Yanhui Liu & Pierre Cizeau & Martin Meyer & Chung-Kang Peng & H. Eugene Stanley, 1997. "Correlations in Economic Time Series," Papers cond-mat/9706021, arXiv.org.
    4. Mech, Timothy S., 1993. "Portfolio return autocorrelation," Journal of Financial Economics, Elsevier, vol. 34(3), pages 307-344, December.
    5. Cizeau, Pierre & Liu, Yanhui & Meyer, Martin & Peng, C.-K. & Eugene Stanley, H., 1997. "Volatility distribution in the S&P500 stock index," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 245(3), pages 441-445.
    6. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    7. Harrison Hong & Jeremy C. Stein, 1999. "A Unified Theory of Underreaction, Momentum Trading, and Overreaction in Asset Markets," Journal of Finance, American Finance Association, vol. 54(6), pages 2143-2184, December.
    8. Toshiaki Watanabe, 2002. "Margin requirements, positive feedback trading, and stock return autocorrelations: the case of Japan," Applied Financial Economics, Taylor & Francis Journals, vol. 12(6), pages 395-403.
    9. Benjamas Jirasakuldech & Riza Emekter & Peter Went, 2006. "Fundamental Value Hypothesis and Return Behavior: Evidence from Emerging Equity Markets," Review of Pacific Basin Financial Markets and Policies (RPBFMP), World Scientific Publishing Co. Pte. Ltd., vol. 9(01), pages 97-127.
    10. Liu, Yanhui & Cizeau, Pierre & Meyer, Martin & Peng, C.-K. & Eugene Stanley, H., 1997. "Correlations in economic time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 245(3), pages 437-440.
    11. Stanley, H. Eugene & Plerou, Vasiliki & Gabaix, Xavier, 2008. "A statistical physics view of financial fluctuations: Evidence for scaling and universality," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(15), pages 3967-3981.
    12. Pierre Cizeau & Yanhui Liu & Martin Meyer & C. -K. Peng & H. Eugene Stanley, 1997. "Volatility distribution in the S&P500 Stock Index," Papers cond-mat/9708143, arXiv.org.
    13. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
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