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2006 | Mathematical, econometrical and computational methods in finance and insurance | 39--50
Tytuł artykułu

Rorecasting Stock Market Indices with Behavioral Trend Equations

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The aim of this article is to present Sornette-Johansen model, its main components and feasible financial applications. In this model the main force that drives stock market indices is the aggregate behaviour of interacting agents who imitate each other's decisions and exchange information. The long-term trend equation used here for the price modelling describes a continuous phase transition between two regimes. One of them represents ordinary trading days, the other precedes stock market crash. The Sornette-Johansen model is based on the notion of the complex system, which is a network of particles (or agents) that repetitively interact. According to this approach, the main concepts which are necessary to forecast changes of long- and middle-term stock market trend are: rational herding, positive feedback, self-organization and critical points. This paper is based on the precursory works of Didier Sornette and Anders Johansen. Both authors have significantly contributed to the development of the theory of complex systems and its applications in physics, economics and social sciences. The article outlines the key steps in derivation of time-dependent trend equations as well as the proposition of estimation method that can be applied in case of noisy data. The first section summarises the main concepts that can be used in order to build a model of a market with endogenous flow of information. The second section describes how the model is derived. In the third section the estimation algorithm and the results obtained for the Polish stock market are presented. (fragment of text)
  • Warsaw School of Economics, Poland
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