Empirical Analysis Of The Fluctuation Of The Shanghai Stock Index Return Rate Based On The ARMA-GARCH Models

This paper uses the Shanghai Composite Index historical data in the period from January 2000 to January 2016.By using the equation of r_t=100*(ln p_t-ln p_t-1),a log return series preprocessing is built.After that,ARMA-GARCH f amily models are established and optimized gradually.Firstly,through the basic statistical analysis,it is found that the log return s eries is a non normal distribution of the left and the ‘peak and thick tail'.Then,by the ADF and PP test the conclusion can be made that the time series is sta tionary,so I build ARMA model to fit the data.In the process of solving the o ptimal fitting model,I need to compare the parameters' significance and the valu es of AIC and BIC under different combination of p and q,so the best fitting model of ARMA?2,3?is built.Through the analysis of the fitting residual seque nce,we can found that the volatility of it sometimes increased and became stabl e insome period of time,Then bythe LM-ARCH test,it can be found that the r esidual sequence's heteroscedasticity can be fitted byGARCH modeling.Secondly,I built ARMA?p,q?-GARCH?m,n?modelsbased on different distri bution state and find the best ARMA-GARCH,ARMA-TGARCH,ARMA-EGAR CH models in different combination ofp,q,m,n.It is found that the model of o ptimal order number combinations both are p=2,q = 2,m = 1,n = 1,andunderthe assumption that the residuals obey the generalized error distribution?GED?a better fitting results can be made.Thirdly,through the comparison of ARMA?2,2?-GARCH?1,1?,ARMA?2,2?-TG ARCH?1,1?and ARMA?2,2?-EGARCH?1,1?,I found that the ARMA?2,2?-TGARCH?1,1?and ARMA?2,2?-EGARCH?1,1?are better than ARMA?2,2?-GARCH?1,1?in terms of prediction and fitting effect.But because the capital market in Chinais affected by the government's policies largely,ARMA-GARCHmodels family are obviously insufficient in the prediction.The index prediction error becomes l arger when it exceeds a certain step number after January 4 in 2016,but ARM A-TGARCH and ARMA-EGARCH modelsindicate that the stock markets will fel l and its volatility will increase.Finally,by solving the values of the loss function,ARMA?2,2?-GARCH?1,1?,ARMA?2,2?-TGARCH?1,1?and ARMA?2,2?-EGARCH?1,1?were evaluated and compared in fluctuation rate forecasting effects.The result is that the ARM A?2,2?-TGARCH?1,1?is best,But due to the constant term in the mean equat ion is not significant,it is necessary to improve it in the basis of ARMA-TGAR CH model.