L. Borodkin
It's not rare case when regression analysis gives no satisfactory explanation of the historical process under consideration. It happens sometimes even we have all factors which could be relevant. Analysing historical time series one should realise that sometimes unexpeted behavior of the system could happen without any substantial external causes. Chaos theory gives an appropriate tool to study unstable social processes which can be characterised by sensitive dependence on initial conditions.
Stock market dynamics is one of “classical” examples of unstable behavior. In our paper we analyse the factors influenced on fluctuating share prices of large Russian joint-stock companies, which securities were quoted in the St. Petersburg stock market between 1900 and 1909 (during the "decade of industrial stagnation" in Russia). We have selected six of the most well-known joint-stock Russian companies: three of them are machine-building companies and three others are oil companies. The primary source for our research was a newspaper Birzhevyie Vedomosti ("The Stock Market News") of St. Petersburg, information from which was used to construct six time series - daily values of share prices of the six companies within the decade. As a result we have about two thousand points for each time series so they are rather long to be analysed by chaos theory methods to detect chaotic behavior.
The main aim of our research is to define the relative role of "internal" factors of the market dynamics, those related to the interrelationships of market players (mostly speculations). To analyse the dynamics of the six time series we used special software "Chaos Data Analyzer: The Professional Version". This program calculates a number of indicators which give a measure of chaos presence (including autoregression function, spectrum function, Lyapunov's λ, etc.).
It should be noted that we detected chaotic behavior in all six time series, however it was expressed more clearly for three machine-building companies. The results permit us to generate the hypothesis of the greater role of "internal" (homogeneous) factors of the functioning of the St. Petersburg stock market.
The main aim of our research is focused on a building a “bridge” between empirical historical observations and sophisticated mathematical models of chaos. We are more optimistic than some other authors in estimation of perspectives of chaos theory applications in historical research.
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