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Stationarity and ergodicity of Markov switching positive conditional mean models

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  • Aknouche, Abdelhakim
  • Francq, Christian

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.

Suggested Citation

  • Aknouche, Abdelhakim & Francq, Christian, 2020. "Stationarity and ergodicity of Markov switching positive conditional mean models," MPRA Paper 102503, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:102503
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    File URL: https://mpra.ub.uni-muenchen.de/102503/1/MPRA_paper_102503.pdf
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    More about this item

    Keywords

    Autoregressive Conditional Duration; Count time series models; finite mixture models; Ergodicity; Integer-valued GARCH; Markov mixture models.;
    All these keywords.

    JEL classification:

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

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