Complex dynamical behaviors of daily data series in stock exchange

It is well known that many economic data series show chaotic behaviors. In this Letter, we further investigate the complex dynamical behaviors of the daily data series, including opening quotation, closing quotation, maximum price, minimum price, and total exchange quantum, in Shenzhen stock exchange and Shanghai stock exchange, which are two representative stock exchanges in mainland China. The maximum Lyapunov exponents, correlation dimensions, and frequency spectra are calculated for these time series. Our results indicate that some daily data series of stock exchanges display low-dimensional chaotic behaviors, and some other daily data series do not show any chaotic behavior. Moreover, we introduce a weighted one-rank local-region approach for predicting short-term daily data series of stock exchange.