Analysis of Nonlinear Characteristics on the Shanghai Stock Market

There are numerous research works on the nonlinear analysis of time series, such as chaotic behavior analysis, heterogeneous variance-covariance structures, etc. However, some studies apply the nonlinear theory to the real financial data without checking the nonlinearity of the time series. In this paper, we detect the nonlinearity by model fitting and confirm the nonlinearity using a statistical test before conducting the analysis of nonlinear characteristics. After confirming the nonlinearity, we then focus on the multifractal analysis of time series and its application to the Shanghai Stock Market. To detect the nonlinear characteristics, the multifractal analysis based on wavelet transform theory is employed in this paper