Financial Data Research Based On Time Series Analysis

With the strengthening of China's economic strength,the financial market is booming.More and more investors are beginning to use mathematical methods to study stock trends,and to predict stocks price.They make full use of theoretical analysis and experience,so as to formulate investment strategies.The main purpose of this dissertation is to analyze the change regular of financial data and predict the financial time series.The financial time series is fitted by the autoregressive moving average(ARMA)model and the residual is fitted by the generalized autoregressive conditional heteroskedasticity(GARCH)model.Taking the daily closing price of the Shanghai Stock Exchange's Shanghai Composite Index as the research object,it is fitted as an ARIMA(3,1,2)model by comparing the information criteria,and the above-mentioned fitted residual sequence is fitted as a GARCH(1,1)model.Since the ARIMA model is based on historical data,in order to involve latest data in to the historical data in time,a rolling prediction method is adopted.In order to select the optimal frequency of model update,seven kinds of step sizes are designed.After comparison,it is concluded that as the step size increases,the average error rate of the prediction increases gradually,and the heteroscedasticity of the residual sequence gradually enhanced.In this dissertation,the model prediction results of step size L=1 and L=3 are analyzed in detail.When L=1,the predicted average error rate does not exceed 0.5%.When L=3,the predicted average error rate is between 0.5% and 0.6%,but it can directly predict the closing price in 3 days,which is more conducive to investment decision.In addition,we also extend the ARIMA rolling prediction of the other six stock indices of the two major domestic stock exchanges.The results are similar to the results of the Shanghai Composite Index analysis,and there are some differences in the average error rate.