A general Markov-Switching autoregressive conditional mean model, valued in the set of non-negative numbers, is considered. The conditional distribution of this model is a finite mixture of non-negative distributions whose conditional mean follows a GARCH-like dynamics with parameters depending on the state of a Markov chain. Three different variants of the model are examined depending on how the lagged-values of the mixing variable are integrated into the conditional mean equation. The model includes, in particular, Markov mixture versions of various well-known non-negative time series models such as the autoregressive conditional duration model, the integer-valued GARCH (INGARCH) model, and the Beta observation driven model. For the three variants of the model, conditions are given for the existence of a stationary and ergodic solution. The proposed conditions match those already known for Markov-switching GARCH models. We also give conditions for finite marginal moments. Applications to various mixture and Markov mixture count, duration and proportion models are provided.

中文翻译：

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马尔可夫切换正条件均值模型的平稳性和遍历性

一般马尔可夫切换自回归条件均值模型，在一组非负数中被考虑。该模型的条件分布是非负分布的有限混合，其条件均值遵循类似 GARCH 的动态，其参数取决于马尔可夫链的状态。根据混合变量的滞后值如何集成到条件均值方程中，检查模型的三种不同变体。该模型尤其包括各种众所周知的非负时间序列模型的马尔可夫混合版本，例如自回归条件持续时间模型、整数值 GARCH (INGARCH) 模型和 Beta 观察驱动模型。对于模型的三个变体，给出了存在固定和遍历解的条件。提出的条件与已知的马尔可夫切换 GARCH 模型相匹配。我们还给出了有限边际矩的条件。提供了对各种混合和马尔可夫混合计数、持续时间和比例模型的应用。