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Study on the fractal and chaotic features of the Shanghai composite index. (English) Zbl 1250.91084
Summary: The Hurst exponent derived by the R/S analysis method of Shanghai stock market’s logarithmic return series is about 0.6298. This shows that the Shanghai stock market exhibits fractal features, and a long memory cycle of about one-and-a-half years. With the reconstruction of phase space, the Shanghai Stock attractor dimension converges to 1.335, which means that the Shanghai stock market has chaotic features, and constructing a dynamic system of the Shanghai stock market needs at least two variables. The findings from the principal component analysis support the conclusion of the existence of chaotic features of the Shanghai stock market. The fractal and chaotic features of the Shanghai stock market reveal the nonlinear properties of the Chinese stock market, and the nonlinearity perspective will be more conducive to the formulation of countermeasures for the development of the Chinese stock market.
MSC:
91B84Economic time series analysis
62M10Time series, auto-correlation, regression, etc. (statistics)
37M10Time series analysis (dynamical systems)
28A80Fractals
37D45Strange attractors, chaotic dynamics