关键词: 估计函数, 联合估计函数, 自回归模型, 时变方差, 伪极大似然估计

Abstract: 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.

Key words: estimation functions, combined estimation functions, autoregressive model, time-varying variance, quasi maximum likelihood estimation