Spatial-temporal Structures And Their Intrinsic Multi-scale Properties In Complex Financial Systems

Financial markets are complex systems with many-body interactions, and have drawn much attention of scientists in various fields. In recent years, much interest of physicists has been paid to the financial dynamics, and physical concepts and methods are applied to analyze the dynamic behavior of financial time series. With large amounts of historical data piled up in the past years, it allows to explore the fine structure of the financial dy-namics and achieve various empirical results. The analysis of multi time scale mentioned in previous studies are about the minutely or daily data. However, the investigation in the intrinsic time scale of the time series are limited. As the time series of financial markets are nonlinear and complex, the fourier spectral analysis and wavelet approach may give misleading results, the empirical mode decomposition (EMD) is an empirical, intuitive, direct and self-adaptive data processing method which is proposed especially for nonlin-ear and non-stationary data. Recent years, the EMD method is applied in many fields, one important application is in financial markets.The EMD method provides us the possibility to investigate the properties of financial markets in intrinsic multi-time scale. With the development of the financial markets in Greater China, a comparative study of the financial markets there becomes important and necessary. It is helpful to understand the spatial-temporal structures, and to understand their intrinsic dynamic mechanisms. Chapters 2,3 and 4 are the main results of our work.In Chapter 1, the history of the international financial markets, especially the stock markets are introduced. Particularly, we give a brief introduction to the development of the econophysics. Then, we show the results already obtained, such as the statistical proper-ties, spatial and temporal correlations. Several significant properties in financial markets are presented, and the development of the comparative study of the western and Chinese markets. In addition, we introduce the current situation of the microscopical models in econophysics. Finally, we show the research motivation and main research results.In Chapter 2, to the best of our knowledge, there have not been literatures focusing on the comparative study of the spatial and temporal structures of the four stock markets in Greater China, although some relevant works could be found such as the comparison between the response dynamics in transition economies and developed countries. In this chapter, we intend to provide a comparative study about the four stock markets. With the random matrix theory, we investigate the spatial and temporal structures of the four stock markets. The sector and subsector structures are studied, and the anti-correlation be-tween the positive and negative subsectors are analyzed. Through investigating the return-volatility correlation of the four indices, we observe that the Chinese markets change to a leverage effect, which indicates that the Chinese markets are becoming mature.In Chapter 3, The analysis of multi time scale mentioned in previous studies are about the minutely or daily data. However, the investigation in the intrinsic time scale of the time series are limited. Through the EMD method we investigate several important properties of financial markets in intrinsic multi-time scale. With the EMD method, a time series can be decomposed into a small number of intrinsic mode functions (IMFs), which are derived based on the local characteristic time scale of the data itself and describe the dynamic behavior from high frequency to low frequency. We investigate the spatial and temporal structures of financial markets in multi time scale with the EMD method, and to understand their intrinsic dynamic mechanisms.In Chapter 4, the IMF decomposed by the EMD method can be seen as a periodic function. For each IMF, the series of amplitude, period and phase can be computed. The dynamics of the amplitude, period and phase time series for each IMF are investigated. Through the study of these characteristics we aim to understanding the moving behavior of the original time series. The probability distributions of the phase differences are computed, and the behaviors that before and after the financial crisis have been investigated.In Chapter 5, the main conclusions are summarized.