Abstract
It is a common phenomenon in the field of financial research to study the dynamic of financial market and explore the complexity of financial system by using various complex scientific methods. In this paper, the chaotic dynamic properties of financial time series are analyzed. Firstly, the nonlinear characteristics of the data are discussed through the empirical analysis of agriculture index data; the daily agriculture index returns can be decomposed into the different scales based on wavelet analysis. Secondly, the dynamic system of some nonlinear characteristic data is established according to the Taylor series expansion form, and the corresponding dynamic characteristics are analyzed. Finally, the bifurcation diagram of the system shows complicated bifurcation phenomena, which provides a perspective for the analysis of chaotic phenomena of economic data.
Highlights
With the development and progress of the society, the financial system we are facing is becoming more and more complex, and the fundamental reason for this complexity is the nonlinearity of the financial system
It is usually difficult to establish mathematical models. It is a common phenomenon in the field of financial research to study the dynamics of financial market and explore the complexity of financial system with various complex scientific methods [1,2,3,4]
Daily price returns have been decomposed into different scales based on the wavelet method
Summary
With the development and progress of the society, the financial system we are facing is becoming more and more complex, and the fundamental reason for this complexity is the nonlinearity of the financial system. It is usually difficult to establish mathematical models It is a common phenomenon in the field of financial research to study the dynamics of financial market and explore the complexity of financial system with various complex scientific methods [1,2,3,4]. Most of the existing research studies about the identification methods of nonlinear dynamic characteristics of data mainly analyze some properties of data from the macro level. As far as we know, there are few studies on the internal structure of financial data from the micro scale of complex dynamic system, and financial data in the index market have not been tested by chaotic dynamics at different time scales. E test has rejected the null hypothesis of chaotic dynamics for the Chinese agriculture index. When we decompose a given agriculture index time series on a scale-by-scale basis, different chaos properties can be found. At the intermediate time scale and long time scale, the test cannot reject the null hypothesis
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