The integer-valued GARCH model is commonly used in modeling time series of counts. Maximum likelihood estimation (MLE) is used to estimate unknown parameters, but numerical results for MLE are sensitive to the choice of initial values, which also occurs in estimating the GARCH model. To alleviate this numerical difficulty, we propose an alternative to MLE and name it as mean targeting estimation (MTE), which is an analogue to variance targeting estimation used in the GARCH model. Consistency and asymptotic normality for MTE are established. Comparisons with the standard MLE are provided and the merits of the mean targeting method are discussed. In particular, it is shown that MTE can be superior to MLE for estimating parameters or prediction when the model is well specified and misspecified. We conduct numerical studies to confirm our theoretical findings and illustrate the practical utility of our proposals.

中文翻译：

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整数值 GARCH(1, 1) 模型的平均目标估计量

整数值 GARCH 模型通常用于对计数的时间序列进行建模。最大似然估计 (MLE) 用于估计未知参数，但 MLE 的数值结果对初始值的选择很敏感，这也发生在估计 GARCH 模型中。为了缓解这种数值困难，我们提出了 MLE 的替代方案，并将其命名为均值目标估计（MTE），它类似于 GARCH 模型中使用的方差目标估计。建立了 MTE 的一致性和渐近正态性。提供了与标准 MLE 的比较，并讨论了平均目标方法的优点。特别是，当模型被很好地指定和错误指定时，MTE 在估计参数或预测方面可以优于 MLE。