Download Piecewise scaling in financial time series and a model of trading

Specialization: 010700/17 Theoretical and Mathematical Physics
Program: 28 The theory of elementary particles and quantum field theory
Head of the program: prof. M. A. Braun
Department of High Energy and Elementary Particles Physics
Scientific Advisor: prof. M. Yu. Pismak
Reviewer: G. A. Chernykh
Piecewise scaling in financial time series and a model
of trading strategies efficiency.
Khalitov Fredis
This paper studies the characteristics of financial processes such as financial time series scaling
and self-organized criticality phenomena. Special kind of piecewise scaling appears in the
calculation of pair correlation functions of financial time series. The study of this phenomenon is
based on direct calculation of correlation functions, as well as within the formal mathematical multiagent model in which financial time series are used as input data. The paper presents the results of
calculations of financial time series piecewise scaling parameters, of numerical experiments to
identify the dynamical mechanisms underlying the scaling, of experiments on the generation of
sequences that have similar characteristics with empirical data. The paper presents the results of
numerical experiments in multi-agent model in which financial time series are used for different
values of model and calculation algorithms parameters.
As the empirical data time series of currency pair EUR/USD for the period 2004.01 – 2006.05
were used.
Summary:
1. Despite their complexity, financial time series have a number of stable characteristics
which are typical for critical dynamics. These include, in particular, break points and slopes of
continuous piecewise linear function that approximates the pair correlation functions of the
actual data in double logarithmic scale.
2. The study of the financial time series reveals mechanisms of the formation of piecewise
scaling dynamics. One of which was studied in detail. A method for generating a time series
that have similar characteristics with empirical data was proposed.
3. Models of critical dynamics can be used in the study of financial processes. A model,
which allows to explore the phenomena of self-organized criticality in financial time series was
developed. Calculations of dynamic characteristics for different values of model parameters
were carried out.
List of publications
1. F. Khalitov. An analysis of empirical data and modeling of processes on a financial market//
International Student Conference “Science and Progress”, St. Petersburg, Russia, Book of
Abstracts, 2010. P. 160.