Stationarity and ergodicity of Markov switching positive conditional mean models

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