时变方差自回归模型的联合估计函数方法推断

A combined estimation functions method for autoregressive model with time-varying variance

针对参数估计问题,利用联合估计函数方法对带有时变方差的自回归模型参数进行统计研究。介绍了带有时变方差自回归模型和联合估计函数理论的研究现状,利用联合估计函数理论,给出带有时变方差自回归模型的参数估计量,证明该参数联合估计量渐近收敛于正态分布。对提出的参数统计量进行数值模拟对比分析,模拟结果表明,与伪极大似然估计量、最小二乘估计量进行对比,提出的参数联合估计量略优于伪极大似然估计量,同时该统计量受误差项分布函数影响较小。

With regard to the problem of parameter estimation,the combined estimation functions method is used to carry out statistical research on the parameter of autoregressive model with time-varying variance.The research status of the autoregressive model with time-varying variance and the combined estimation functions theory is reported.The combined estimation functions theory is used to obtain the parameter estimators of the autoregressive model with time-varying variance,and it is proved that the parameter estimators of the combined estimation functions method asymptotically converge to normal distribution.The numerical simulation is carried out for the comparative analysis of the proposed parameters.The simulation results show that,compared with the quasi maximum likelihood estimators and the least squares estimators,the proposed parameter estimators of combined estimation functions are slightly better than those of quasi maximum likelihood estimation,and the statistic is less affected by the distribution function of error terms.