VaR Comparison for Fractal Diffusion System using R/S Method

Causal analysis is difficult in economics, finances and other social fields because of the complexity of these systems. U sing a fractional-order chaotic system as a causal relationship structure to present a dataset, the key parameters of the fractional Brownian motion and W eierstrass- Mandelbrot function (WMF) with feedback term come from the dataset fixedly or randomly, meaning the unchanging structure or the variable structure of these data, respectively. RlS method and VaR are used to compare the hurst exponent of the three datasets generated by the random distribution, the fractional Brownian motion and WMF. The result shows that when the structure of the underline WMF changes, its time sequences illustrate the normal distribution for the lower observation frequency while a long-term memory effect for the higher observation frequency. It also indicates that nonlinear system theory, fractal theory, and control theory will play a crucial role in profoundly revealing the causal mechanisms of complex social systems such as economy and finance.