An Empirical Analysis Of Shanghai Composite Index Based On ARIMA-GARCH Model

In the field of time series research,it is very practical to carry out modeling analysis and explore the law of the changing volatility of asset yield.In stock securities and other financial markets,volatility is the standard deviation of the standard rate of return on assets.As a measure of asset risk,volatility is often used to measure the size of asset risk.The conditional variance of the asset yield is different from that in the ARIMA process.When the time interval is equal,the variance is constant,and the conditional variance will change with the current and past values.It is a random process,and the volatility itself.Some characteristics,such as volatility aggregation and leverage,are used to analyze the relevant characteristics of volatility,and the volatility is predicted by the model,which can provide reference for investment decision.In this paper,the ARIMA-GARCH model is used to model the daily closing price of the stock index.The logarithmic transformation and first order difference is processed,converting a time series to a stable one.The economic significance is the volatility of the asset yield,also known as the index yield,through the stability of the index yield test,and select the appropriate order to establish ARIMA model;and the residual effect ARCH,through the establishment of GARCH model to eliminate heteroskedasticity.In this paper,based on the theory of time series analysis,the exponential rate of return of the Shanghai Composite Index is established.Through the analysis of the timing chart,we can see that the exponential yield sequence has fluctuating cluster effect.By analyzing the ACF and PACF,the ARMA(6,0)model was established for the exponential yield sequence.In the process of residual test,the heteroskedasticity of the sequence was verified,and the heteroskedasticity of the sequence was eliminated by establishing the GARCH(1,1)model.The residuals of the model are compared with the normal distribution and the skew t-student distribution.The EGARCH(1,1)model is used to verify that the yield series has a "leverage effect".