Catastrophe theory and price dynamics
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Catastrophe theory and price dynamics
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Viktor Balyabin 
Affiliation: MEI
Address: Russian Federation, Moscow
Aleksey Zaslavsky
Affiliation: CEMI RAS
Address: Russian Federation, Moscow
The paper is about finance markets research using non-classical non-linear dynamic methods. Classical time series (including market trends) prediction and analyses methods are based on mathematical statistics. These methods are based on linear and non-linear regression, moving averages and others. Statistical approach assumes that input data honors the normal distribution law. Practice shows that market trends data form normal distribution only on quiet market form and prediction of abrupt shifts is more valuable and important for market analytics. With the evolution of mathematics and social sciences, economists began to apply the differential calculus and its most complicated part – non-linear dynamics – long-known in physics. Starting with Benoit Mandelbrot 1960s works, scientists and analytics widely apply non-linear methods in market terms researches. Mandelbrot started with fractals and power laws; the researches nowadays also apply chaos and catastrophe theory. Catastrophe theory is a big mathematics nonlinear discipline. Catastrophe in terms of mathematics is a discontinuous shift of a system in response to small parameter change. In this paper we apply catastrophe theory to market quotes dynamics. We take market demand and supply as control parameters and trend reverse – as catastrophe. We constructed theoretical model and tested it on real data of property market.
nonlinear dynamics, catastrophe theory, assembly-type catastrophe, condition variable, control parameters
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