Chaos theory in financial time series analysis – theoretical aspects and empirical researches

Krzysztof Jajuga, Daniel Papla
Dynamiczne Modele Ekonometryczne
V Ogólnopolskie Seminarium Naukowe, 9-11 września 1997 r. w Toruniu
Katedra Ekonometrii i Statystyki, Uniwersytet Mikołaja Kopernika w Toruniu
In his post-conference paper authors present the basic assumptions and methods of chaos theory that can be possibly used in market analyses. At first they place those methods among others quantity methods which have been worked out due to predict the certain market variables like price of commodities. Those are: technical analysis, stochastic methods, methods of financial cybernetic, econometric methods and chaos theory. The common feature of those methods is the abortion of the effective market hypothesis. In other words, they assume that the information of the past prices do not affect the present value.
The authors describe briefly what is deterministic chaos and what sort of mathematical methods of that theory can be applied to market analysis. Two of them are presented in details. Those are: correlative dimension and Hurst’s exponent.
At the end both methods are applied to the share prices on the Polish stock exchange within 1994 – 97. The results are ambiguous. It may suggest that there exists no attractor, what is the necessary condition to make the accurate predictions, or that the set of data is not rich enough.
They conclude that the example of stock exchange shows clearly the difference between the use of chaos theory in physics and in economics.
The paper is a very brief but comprehensive presentation of certain quantity methods used in market analyses. Although the methods are very sophisticated, while they are applied in practice, the results are very poor. Fortunately the authors acknowledge that.


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