Dynamics of market indices, Markov chains, and random walking problem

Details Dynamics of market indices, Markov chains, and random walking problem Dynamics of market indices, Markov chains, and random walking problem

2001-12-16

arxiv.org/abs/physics/0112045v1

Physics

Physics and Society

Talk given at the Conference "Applications of Physics in Financial Analysis" (5 - 7 December 2001, London), 27 pages, LaTeX

Scientific paper

Dynamics of the major USA market indices DJIA, S&P, Nasdaq, and NYSE is analyzed from the point of view of the random walking problem with two-step correlations of the market moves. The parameters characterizing the stochastic dynamics are determined empirically from the historical quotes for the daily, weekly, and monthly series. The results show existence of statistically significant correlations between the subsequent market moves. The weekly and monthly parameters are calculated in terms of the daily parameters, assuming that the Markov chains with two-step correlations give a complete description of the market stochastic dynamics. We show that the macro- and micro-parameters obey the renorm group equation. The comparison of the parameters determined from the renorm group equation with the historical values shows that the Markov chains approach gives reasonable predictions for the weekly quotes and underestimates the probability for continuation of the down trend in the monthly quotes. The return and its dispersion for the "buy-and-hold" and "follow-trend" strategies are calculated. The problem of how to combine these two strategies to reduce the dispersion is discussed and its analytical solution is proposed. The results of the constructing a "computer-based" strategy which combines the series analysis with the candlesticks charting techniques are reported.

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