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

B. D. Craven and Sardar M. N. Islam ()
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B. D. Craven: Department of Mathematics & Statistics, University of Melbourne, Victoria 3010, Australia
Sardar M. N. Islam: VISES, Victoria University, Melbourne, Victoria 8001, Australia

Review of Pacific Basin Financial Markets and Policies (RPBFMP), 2015, vol. 18, issue 04, 1-12

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.

Keywords: Stock price; trend; modeling; fluctuations (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1142/S0219091515500277

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