带相依辅助信息的分位数自回归模型的经验似然估计

Empirical likelihood for quantile autoregressive models with dependent auxiliary information

分位数自回归模型作为一类常用的变系数时间序列模型,在理论研究和实际问题中都有广泛的应用.考虑到这类模型具有自回归的结构属性,数据采集过程中产生的额外信息,以相依辅助信息函数的形式被引入到模型系数的估计中来.该文应用经验似然方法得到了模型系数的估计量,得到了模型系数的估计量,并论证了其渐近正态性.基于渐近正态性的理论结果,进一步讨论了模型系数线性约束性问题的Wald检验统计量的渐近性质.数值模拟和实例数据分析的结果均表明,利用经验似然估计处理带相依辅助信息函数的方法较传统的分位数回归估计更有效.因而,一般常系数线性分位数回归模型在独立假设下的结果,被推广至具有相依结构的一类变系数模型中去.

Quantile autoregressive(QAR)models,commonly adopted in varying-coefficients time series modelling,has been shown its popularity in both theoretical and empirical studies.Equipped with autoregressive structure,QAR models sometimes involve extra information in the data collection process which is known as dependent auxiliary information.An empirical likelihood approach is used to construct the quantile estimates.The asymptotic normality of the estimates is established conditionally on the lagged values of the response.Under the framework of empirical likelihood method with dependent auxiliary information,the Wald test statistics are developed for testing the linear restriction on the parameters.Both the simulation and the empirical study results indicate that the proposed method yields more efficiency than the traditional one.Therefore,the results for general constant coefficients QAR model under independent and identically distributed assumptions could be extended to a class of varying coefficients QAR model with dependent structure.