Study On The Nonlinear Characteristics Of Stock Index Futures In China Based On Fractal Theory

Based on the fractal market theory of nonlinear dynamical systems, this paper uses the yield of the stock index futures market as the research object, tests the validity of the stock index futures market, reveals its fractal structure characteristics, and then analyses the yields and volatility of the double length memory.According to the theoretical introduction, first apply R/S analysis of single fractal method to calculate the Hurst exponent of China’s stock index futures market daily and weekly return series. Then define that there are obvious fractal characteristics in our stock index futures market, namely the market has long-term memory feature, recent price and market information will have continuous long-term effects for the market, and it will last longer. Then, compare the analysis st-abilities of three R/S analysis to determine the classic R/S analysis method which is suited to calculate the daily and weekly yield Hurst index, and finally measure long memory index futures market yields itself has. Secondly, for the spike, thick tail, asymmetrical features of stock index futures yields and the long memory characteristics of conditions volatility, an ARFIMA-HYGARCH models is applied to analyze them. Different from the past traditional method, the POT model of EVT theory is used to set the threshold. Then apply the extreme value theory to construct a model for the standard yield tail of the distribution. Based the extreme risk of the domestic stock index futures market on the above, this paper is measured by back testing checks to ensure the reliability and stability of the risk model.The empirical results show that China’s stock index futures yields sequences and conditional volatility rates exist vary degrees of long memory features. For the normal distribution, skewed distribution and student distribution, the ARF1MA-HYGARCH-EVT model has certain advantages, mainly reflected in the risk detection with good accuracy and stability. The model can avoid risks to a certain extent. Investors, government and risk managers can also use this model to make quantitative analysis, so as to make ARFIMA-HYGARCH-EVT model better prevent risk, manage and control risks and ensure the healthy growth of the stock index futures market.Finally, based on the conclusion of double long memory in stock index futures market, the paper describes the impact for the fractal characteristics of the China’s stock index futures market and puts forward reasonable suggestions.