We consider integer-valued processes with a linear or nonlinear generalized autoregressive conditional heteroscedastic models structure, where the count variables given the past follow a Poisson distribution. We show that a contraction condition imposed on the intensity function yields a contraction property of the Markov kernel of the process. This allows almost effortless proofs of the existence and uniqueness of a stationary distribution as well as of absolute regularity of the count process. As our main result, we construct a coupling of the original process and a model-based bootstrap counterpart. Using a contraction property of the Markov kernel of the coupled process we obtain bootstrap consistency for different types of statistics.

中文翻译：

---

整数值 GARCH(p, q) 进程的引导程序

我们考虑具有线性或非线性广义自回归条件异方差模型结构的整数值过程，其中给定过去的计数变量遵循泊松分布。我们表明，强加在强度函数上的收缩条件会产生该过程的马尔可夫核的收缩特性。这几乎可以毫不费力地证明平稳分布的存在性和唯一性以及计数过程的绝对规律性。作为我们的主要结果，我们构建了原始过程和基于模型的引导对应物的耦合。使用耦合过程的马尔可夫核的收缩特性，我们获得了不同类型统计数据的引导一致性。