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Autoregressive processes with data‐driven regime switching

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  • Joseph Tadjuidje Kamgaing
  • Hernando Ombao
  • Richard A. Davis

Abstract

. We develop a switching‐regime vector autoregressive model in which changes in regimes are governed by an underlying Markov process. In contrast to the typical hidden Markov approach, we allow the transition probabilities of the underlying Markov process to depend on past values of the time series and exogenous variables. Such processes have potential applications in finance and neuroscience. In the latter, the brain activity at time t (measured by electroencephalograms) will be modelled as a function of both its past values as well as exogenous variables (such as visual or somatosensory stimuli). In this article, we establish stationarity, geometric ergodicity and existence of moments for these processes under suitable conditions on the parameters of the model. Such properties are important for understanding the stability properties of the model as well as for deriving the asymptotic behaviour of various statistics and model parameter estimators.

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  • Joseph Tadjuidje Kamgaing & Hernando Ombao & Richard A. Davis, 2009. "Autoregressive processes with data‐driven regime switching," Journal of Time Series Analysis, Wiley Blackwell, vol. 30(5), pages 505-533, September.
    • Handle: RePEc:bla:jtsera:v:30:y:2009:i:5:p:505-533
    DOI: 10.1111/j.1467-9892.2009.00622.x
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    References listed on IDEAS

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    6. Davis, Richard A. & Lee, Thomas C.M. & Rodriguez-Yam, Gabriel A., 2006. "Structural Break Estimation for Nonstationary Time Series Models," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 223-239, March.
    7. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-384, March.
    8. Stockis, Jean-Pierre & Tadjuidje-Kamgaing, Joseph & Franke, Jürgen, 2008. "A note on the identifiability of the conditional expectation for the mixtures of neural networks," Statistics & Probability Letters, Elsevier, vol. 78(6), pages 739-742, April.
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    Cited by:

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    2. Jaehee Kim & Sooyoung Cheon, 2010. "A Bayesian regime‐switching time‐series model," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(5), pages 365-378, September.
    3. Augustin Kelava & Pascal Kilian & Judith Glaesser & Samuel Merk & Holger Brandt, 2022. "Forecasting Intra-individual Changes of Affective States Taking into Account Inter-individual Differences Using Intensive Longitudinal Data from a University Student Dropout Study in Math," Psychometrika, Springer;The Psychometric Society, vol. 87(2), pages 533-558, June.
    4. Francesco Battaglia & Mattheos Protopapas, 2012. "An analysis of global warming in the Alpine region based on nonlinear nonstationary time series models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 21(3), pages 315-334, August.
    5. Demian Pouzo & Zacharias Psaradakis & Martin Sola, 2022. "Maximum Likelihood Estimation in Markov Regime‐Switching Models With Covariate‐Dependent Transition Probabilities," Econometrica, Econometric Society, vol. 90(4), pages 1681-1710, July.
    6. Francesco Battaglia & Mattheos Protopapas, 2012. "Multi–regime models for nonlinear nonstationary time series," Computational Statistics, Springer, vol. 27(2), pages 319-341, June.

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