We propose a GARCH model for uncorrelated, integer-valued time series that exhibit conditional heteroskedasticity. Conditioned on past information, these observations have a two-sided Poisson distribution with time-varying variance. Positive and negative observations can have an asymmetric impact on conditional variance. We give conditions under which the proposed integer-valued GARCH process is stationary, ergodic, and has finite moments. We consider maximum likelihood estimation for model parameters, and we give the limiting distribution for these estimators when the true parameter vector is in the interior of its parameter space, and when some GARCH coefficients are zero.

中文翻译：

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整数值非对称 garch 建模

我们为表现出条件异方差性的不相关整数值时间序列提出了 GARCH 模型。以过去的信息为条件，这些观察结果具有随时间变化的方差的两侧泊松分布。正面和负面观察可能对条件方差产生不对称的影响。我们给出了所提出的整数值 GARCH 过程平稳、遍历且具有有限矩的条件。我们考虑模型参数的最大似然估计，并且当真实参数向量在其参数空间内部时，并且当一些 GARCH 系数为零时，我们给出这些估计量的极限分布。