Estimation And Application Of Quantile Autoregressive Model With Dependent Auxiliary Information

Since Koenker and Bassett(1978)proposed quantile regression,Quantile regression has been widely applied to many different fields for its excellent statistical properties.Tang and Leng(2012)apply it to ordinary linear models by quantile empirical likelihood method with auxiliary information,obtaining the estimations of quantile regression coefficients of the models,and making the statistical inference.Inspired by this,the Quantile Autoregression Model(QAR)is studied in this paper.Compared with the traditional constant coefficient autoregressive time series model,the coefficients of QAR model contains dynamic random variable.At the same time,the model itself has a dependent structure,so the existing independent identical distribution results can't be translated into the QAR model in statistical inference.Therefore,we obtain the estimations of the autoregressive coefficients of the model by means of auxiliary information in the framework of empirical likelihood,and their asymptotic normality is derived.It is worth mentioning that for QAR being an autoregressive model,the allowable variables in the auxiliary information set up in this paper are dependent,and the results demonstrated in this paper degenerating to the constant coefficient time series model are also true.In order to verify the conclusion of this paper,we carry out the numerical simulation and empirical analysis at the end of the paper.In the part of numerical simulation,the estimations of regression coefficients are calculated for different error models where the sample containers are offered with 100,250,500.Besides,compared with the existing methods,the proposed method improves the effectiveness of coefficient estimation.In the case analysis,the US unemployment rate is selected for QAR modeling.From the point estimation and the length of interval estimation,the validity of the method is demonstrated.