We propose a new model for nonstationary integer-valued time series which is particularly suitable for data with a strong trend. In contrast to popular Poisson-INGARCH models, but in line with classical GARCH models, we propose to pick the conditional distributions from nearly scale invariant families where the mean absolute value and the standard deviation are of the same order of magnitude. As an important prerequisite for applications in statistics, we prove absolute regularity of the count process with exponentially decaying coefficients.

翻译：我们提出一种适用于非平稳整数值时间序列的新模型，尤其适合含强趋势的数据。与流行的泊松-INGARCH模型不同，但遵循经典GARCH模型的思路，我们提出从近似尺度不变族中选取条件分布，其中均值绝对值与标准差处于同一量级。作为统计学应用的重要前提，我们证明了该计数过程具有指数衰减系数的绝对正则性。