Dynamic VaR Estimation On AQI Of Chongqing By ARFIMA-GARCH-F Models

Under the guidance of reform and opening up,and the western expansion and oth-er policies,Chongqing’s economy has been growing rapidly in recent years.While industrial modernization has caused atmosphere environments to be damaged seri-ously.The Meteorological Department of Chongqing has issued haze early warning since 2014 with eight haze warning signals from 2014 to 2015.Serious air pollu-tion has brought many healthy problems to citizens.The air quality index(AQI)represents one of the atmospheric environmental quality evaluation criteria,which shows that the higher of the AQI index is,the worse the quality of the environment is.In this paper,sample of the AQI index is from January 1,2014 to December 31,2015.In order to show the data generating of the AQI index sequence,we us ARFIMA to model AQI mean equation and use GARCH to model its volatil-ity variance equation,respectively.For the residuals,we assume that its follows the F distribution such as normal distribution,skew-normal distribution,T distri-bution,skew-T distribution.Parameters estimation,Random simulation,and the VaR estimation are compared respectively under each ARFIMA-GARCH-F model.Empirical analysis shows that the ARFIMA-GARCH-T/skew-T are superior to the ARFIMA-GARCH-normal/skew-normal as we fit the AQI index and estimate the dynamic VaR by using extreme value theory.Therefore,we can use VaR estimation by using extreme value theory as the method of calculating the high quantile in case of lacking information the distribution of residuals.In addition,the more accurate the model fitting is,the better forecast the dynamic VaR can be.