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Student
Title
Supervisor
Faculty
Educational Programme
Final Grade
Year of Graduation
Bogdan Mysiv
Qualitative Characteristics of the Low-dimensional Chaos from Financial Time Series
Business Informatics
(Bachelor’s programme)
2017
This work is devoted to the search of qualitative characteristics of low-dimensional chaos in financial time series. The relevance of the research lies in the fact that modern researches in the economic and financial sphere are based on linear models. However, in reality, they are not linear, so it is necessary to try to simulate the current problems with the help of nonlinear equations.

The purpose of the study is to study various time series, to ascertain their "chaotic" origin, to find qualitative characteristics of low-dimensional chaos and to give them a logical interpretation. To achieve these goals, the following tasks are set:

1) Calculation of the correlation dimension;

2) Restoration of the attractor;

3) The image of a three-dimensional phase space;

4) Construction of autocorrelation function;

5) Construction of the function of average mutual information;

6) Calculation of the Hurst index.

The object of the study is the financial time series generated by the international currency exchange market. The subject of the study is the qualitative characteristics of low-dimensional chaos in the series in question.

During the project, five different time series were studied: the exchange rates of CAD, GBP, GHF, INR, YEN against the US dollar for the last 47 years. The dimension of each sample of cargo is more than 104.

To process the financial time series and obtain the relevant indicators, the Fractan software was used.

As a result, the difference between stochastic and chaotic time series was explained. Secondly, it was proved that the observed time series have a dynamic nature by means of restoring the attractor and estimating the correlation dimension. Thirdly, qualitative characteristics of low-dimensional chaos were observed in all observed series and interpretations of these characteristics were given. A quantitative sign of low-dimensional chaos, the Hurst index, was also considered.

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