Aknouche, Abdelhakim and Francq, Christian
(2020):
*Stationarity and ergodicity of Markov switching positive conditional mean models.*

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## Abstract

A general Markov-Switching autoregressive conditional mean model, valued in the set of nonnegative numbers, is considered. The conditional distribution of this model is a finite mixture of nonnegative 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 nonnegative time series models such as the autoregressive conditional duration (ACD) model, the integer-valued GARCH (INGARCH) model, and the Beta observation driven model. Under contraction in mean conditions, it is shown that the three variants of the model are stationary and ergodic when the stochastic order and the mean order of the mixing distributions are equal. 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.

Item Type: | MPRA Paper |
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Original Title: | Stationarity and ergodicity of Markov switching positive conditional mean models |

English Title: | Stationarity and ergodicity of Markov switching positive conditional mean models |

Language: | English |

Keywords: | Autoregressive Conditional Duration, Count time series models, finite mixture models, Ergodicity, Integer-valued GARCH, Markov mixture models. |

Subjects: | C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C10 - General C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C18 - Methodological Issues: General C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables > C22 - Time-Series Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables > C25 - Discrete Regression and Qualitative Choice Models ; Discrete Regressors ; Proportions ; Probabilities |

Item ID: | 102503 |

Depositing User: | Prof. Abdelhakim Aknouche |

Date Deposited: | 23 Aug 2020 20:26 |

Last Modified: | 23 Aug 2020 20:26 |

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URI: | https://mpra.ub.uni-muenchen.de/id/eprint/102503 |