The Grey Fractals And Econometric Models And Its Application In CSI300 Market

There is more and more research show that the financial market is a complex, nonlinear, multi-body system with many stylized facts. Those are not corresponding to some of the basic assumptions of traditional financial theory, which need multidisciplinary theories and methods to have a relatively comprehensive and profound understanding of financial markets. The Econophysics and Economics are two mainstream directions to solve the problem of financial market. In this paper, based on the existing Econophysics and Economics theory and methods, we improve the method in Econophysics and Economics combining some characteristics of financial markets, which enrich the existing modeling method system. Using those new methods, we study the CSI300 spot and future market’s multifractal, market efficiency, Va R risk measure, and the realized volatility forecasting, which provides the reference for the market investment and risk management. The main research contents and achievements are as follows:(1)In this part, we firstly analyze the nature of partition function and the multifractality parameters’ economic meaning. Meanwhile, on account of traditional partition function hardly applying to the condition that the time series length T is a prime number or cannot be divisible by scaling s; we put forward a modified partition function whose algorithm procedure is similar to MFDFA. Using the Numerical Simulation of binomial multifractality, the result shows that the new method dealing with the multifractality of time series whose length is prime number is feasible and effective. By applying modified partition function, we investigate the multifractality of CSI300 spot. Through shuffling, removing extreme values and iterating amplitude adjusted flourier transform technological, we find that the factors of the multifractality. So, the modified partition function can be used in real problem.(2)In this part, we construct the grey operation under the framework of grey buffer operator and grey adjustment coefficient, and put forward the detrending weighted moving algorithm(DWMA). Numerical simulation on fractal noise with fluctuation and linear trend shows that detrending moving average algorithm(DMA) is not the optimal method to calculate Hurst on accuracy; it is only a special case of DWMA. The centered detrending moving weighted algorithm(λ = 6, θ = 0.5) can effectively remove the sequence trend, the accuracy of calculating Hurst value is also higher. In Empirical analysis, we investigate the long memory of realized volatility of CSI300 spot and future by the DWMA method.(3) In this part, we apply the multifractal weighted detrending moving average(MFDWMA) to investigate and compare the efficiency and multifractality of CSI300 spot and future. The results show that the spot market becomes closer to weak-form efficiency after the introduction of index future. We find that the spot is featured by multifractality and there is less complexity and risk after the index future was introduced. Using the method of rolling windows, we investigate the asymptotic efficiency of index future, and find that the future market is not efficient at the beginning of listing, and then it becomes efficient, but now is a little from efficient. Besides, using the traditional linear Granger causality test and the nonlinear Granger causality developed by non-parametric test method, we research the interaction between the stock index spot and futures under different periods. The results show that there are linear and nonlinear Granger causality in entire period of the study. At the beginning of future listed on market, there are double-way linear Granger causality between stock index spot and future, and future market has one-way nonlinear Granger causality on the spot market. In the next different stages, the linear and nonlinear Granger relationship of future market on the spot is still significant, but the linear and nonlinear Granger relationship of spot market on future is gradually weakened. That’s to say, as the market continuing to deep, future market leads the role of price discovery from linear and nonlinear viewpoint.(4)In this part, in the view of events time, we study volatility returns and trading volume interval of CSI300 spot and future market by the complicated method, the results shows that the probability distributions of the volatility returns and trading volume intervals have a uniform scaling curve for different threshold value q. The tail of scaling curve can be well fitted by the stretched exponential function. Both shot-term and long-term memory effects are observed in the recurrence intervals different thresholds q. In addition, we analysis the relation between trading volume and volatility interval, and indicate that large volatility and large volume is synchronous. We also discuss the application in risk management, and suggest that the duration model(ACD) should be modeled in recurrence intervals analysis.(5) In this part, some typical facts of the CSI300 spot and future are verified using the method of econophysics, then different GARCH models measuring Va R risk under different distributions are estimated, further, we use the Kupiec LR test and dynamic quantile regression to test the Va R measurement. For the spot, the results show that the return distribution is far from normal distribution, Long memory of return is not obvious, but the volatility is strong. The model with the return distribution of Skew Student t distribution measuring the reliability of Va R is significantly higher than that in normal distribution and t distribution. Whether within the sample or out of the sample, HYGARCH model can give more accurate measurement when Va R level is higher. So, HYGARCH model with Skew Student t distribution which captures more typical facts of financial assets can give more accurate and reliable Va R measurement for HS 300 index. For index future, the asymmetry of return distribution is not significant, but there are peak and thick tail in distribution, its distribution is also far from the normal distribution. Similarly, index future returns almost does not exist long memory, but volatility has significant long memory. Whether out of sample or in sample, Va R measure model’s precision with distribution obeying t distribution and Skew Student t distribution are higher than the normal distribution, which is corresponding to the symmetry of the return distribution, and Va R measurement under GJR model is the most effective.(6)As the distribution of CSI300 spot and future logarithmic realized volatility is far from the normal distribution, we use Skew Student t distribution which can characterizes more feature of sequence distribution to fit the logarithmic realized volatility. Meanwhile, based on the typical facts the existence of financial market, we use more GARCH models to fit the conditional heteroscedasticity of logarithmic realized volatility models. Under different loss functions, the models’ prediction ability with different distributions and different models are evaluated by MCS test method. The results show that, the forecasting results of volatility model with Skew Student t distribution is more accurate than normal distribution, and ARFIMAX or ARFIMAX-GARCH models can provide good prediction accuracy. For the index future, we obtain similar results. The studying enriches the realized volatility modeling system, and provides a new method for forecasting volatility.