Portmanteau Test And Its Pplication Of ARFIMA-GARCH Model

With the development of the information age and network technology, the ability,which time series data is processed is becoming more and more powerful. However,in practical applications, modeling and statistical inference for time series data is still concerned. Due to the time series data existing some characteristics that is long and short memory, heteroscedasticity, it needs to choose a right time series model to fit.If the model is not appropriate, it will make a serious prediction error. Therefore, the model needs to have a diagnostic test. Recent years, people began to use portmanteau test to test model. Portmanteau test is gradually becoming a tool of diagnostic test.Portmanteau test is paid attention in finance. Many scholars have studied it. It shows that portmanteau test based on quasi-maximum exponential likelihood estimation can better test whether or not the fitting model is accurate and meets the actual data.In this paper, based on ARFIMA-GARCH model, portmanteau test, mix portmanteau test and its application are researched for quasi-maximum exponential likelihood estimation.The theory of ARFIMA-GARCH model, the definition and the main properties of quasi-maximum exponential likelihood estimation and portmanteau test are introduced. For quasi-maximum exponential likelihood estimation of ARFIMA-GARCH model, the limiting distribution of squared residual autocorrelation functions is given,and then portmanteau test based on squared residual autocorrelation functions is constructed. And the asymptotic distribution is given. Then, on the basis of the residual and squared residual autocorrelation functions, the joint limiting distribution of the residuals autocorrelation functions and squared residuals autocorrelation functions is provided. A mix portmanteau test is further constructed. Its asymptotic distribution is also given.By analyzing the stationary, the correlation and the heteroscedasticity of the sample data, AR-GARCH model is established with quasi-maximum exponential likelihood estimation. And portmanteau test and mix portmanteau test, which is given in this paper, are carried out to diagnostic test the fitting AR-GARCH model. Results show that portmanteau test based on the squared residual autocorrelation functions and mix portmanteau test based on the residual and the squared residual autocorrelation functions are applied to diagnostic test time series model fitted by quasi-maximum exponential likelihood estimation.