Nonlinear Structure in Shanghai Stock Index

The typical character of financial market is nonlinear. The nonlinear structure in financial market is explored through the method of time-series analysis and the theory of nonlinear dynamics. The empirical result shows that return series of Shanghai Stock Index is a little degree of freedom chaos system with self-similar nonlinear structure. The nonlinear structure cannot be simulated adequately by ARCH(4) model, however, GARCH(1,1) and EGARCH(1,1) model can mimic the nonlinear structure better than other models.