Forecast On The Volatility Of A-stock Index Return Rate

The main purpose of this paper is to forecast the volatility of the A-Stock market return rate which is computed by the daily closing price data of the Shanghai Composite Index in the last ten years.The main methods used are the GARCH model family and the vSVM algorithms.First,the logarithmic yield time series is modeled using the ARMA-GARCH and ARMA-EGARCH models of the time series models.After the basic statistical analysis of the logarithmic yield series,the non-normal distribution pattern of the "peak and the left" is found.Then,through the statistical test,I found that the series is not white noise and the series is stable,so I can use the ARMA model to fit the series.Statistical analysis of the residual series after ARMA modeling shows that the residual series is not white noise too,and there are obvious ARCH effects showed in the statistical test report,so there are some useful information can be extracted.Also the statistical test shows that the autocorrelation of the residual series is in a long-term,I use the GARCH model family to fit the residual series of the ARMA model.According to the previous research results,the GARCH(1,1)model has a relatively good performance in predicting the volatility of financial time series,and the model is simple and practical.The EGARCH model makes up for the inadequate of the standard GARCH model and can reflect the different impact of positive and negative impact on the volatility of the market-the leverage effect of financial markets.In this paper,the residual sequence after modeling the ARMA model is modeled by GARCH(1,1)model and EGARCH(1,1)model.Secondly,the data-driven method-the support vector machine algorithm is used to predict the volatility.In this paper,vSVM algorithm,normalized-vSVM,and wavelet-vSVM support vector algorithm are used to predict the volatility from different perspectives of data processing and analysis.Among them,vSVM is a improved SVM algorithm,firstly proposed by Scholkolf.Normalized-vSVM is a vSVM algorithmin using the normalized data.The Wavelet-vSVM is a vSVM algorithmin using the wavelet kernel to descibe the multi-scale feature of financial data.Then adjust the parameters of the four models to achieve a better prediction performance.Finally,for the different models,two kinds of loss function-the mean square errorand the mean absolute error are used to compare and analyze the prediction performance of different models.The result shows that the vSVM algorithm after data processing is slightly better than the traditional GARCH(1,1)model and the EGARCH(1,1)model,and the performance of the normalized-vSVM algorithm is optimal in all the models in this paper.