IDEAS home Printed from https://ideas.repec.org/a/eee/ecolet/v232y2023ics0165176523003828.html
   My bibliography  Save this article

Impulse response function analysis for Markov switching var models

Author

Listed:
  • Cavicchioli, Maddalena

Abstract

We exactly derive the regime-dependent impulse response functions for a Markov switching vector autoregression (VAR) model in terms of neat matrix expressions in closed form. The key is to recognize that the latent first-order Markov switching process in the model has a VAR(1) representation, and that the model can be cast into a state-space form. Using such a representation, the regime-dependent impulse response function analysis can be processed with respect to either an asymmetric discrete shock or to a symmetric continuous shock. Our results extend and correct those obtained by Ehrmann et al. (2003) and coincide with those by Hamilton (1994) for the case of standard VAR models.

Suggested Citation

  • Cavicchioli, Maddalena, 2023. "Impulse response function analysis for Markov switching var models," Economics Letters, Elsevier, vol. 232(C).
    • Handle: RePEc:eee:ecolet:v:232:y:2023:i:c:s0165176523003828
    DOI: 10.1016/j.econlet.2023.111357
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0165176523003828
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.econlet.2023.111357?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Karamé, F., 2010. "Impulse-response functions in Markov-switching structural vector autoregressions: A step further," Economics Letters, Elsevier, vol. 106(3), pages 162-165, March.
    2. Karamé, F., 2012. "An algorithm for generalized impulse-response functions in Markov-switching structural VAR," Economics Letters, Elsevier, vol. 117(1), pages 230-234.
    3. Jing Zhang & Robert A. Stine, 2001. "Autocovariance Structure of Markov Regime Switching Models and Model Selection," Journal of Time Series Analysis, Wiley Blackwell, vol. 22(1), pages 107-124, January.
    4. Ehrmann, Michael & Ellison, Martin & Valla, Natacha, 2003. "Regime-dependent impulse response functions in a Markov-switching vector autoregression model," Economics Letters, Elsevier, vol. 78(3), pages 295-299, March.
    5. Cavicchioli, Maddalena, 2017. "Asymptotic Fisher information matrix of Markov switching VARMA models," Journal of Multivariate Analysis, Elsevier, vol. 157(C), pages 124-135.
    6. Zhuo Qiao & Yuming Li & Wing-Keung Wong, 2011. "Regime-dependent relationships among the stock markets of the US, Australia and New Zealand: a Markov-switching VAR approach," Applied Financial Economics, Taylor & Francis Journals, vol. 21(24), pages 1831-1841, December.
    7. Zhongjun Qu & Fan Zhuo, 2021. "Likelihood Ratio-Based Tests for Markov Regime Switching," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 88(2), pages 937-968.
    8. Kasahara, Hiroyuki & Shimotsu, Katsumi, 2019. "Asymptotic properties of the maximum likelihood estimator in regime switching econometric models," Journal of Econometrics, Elsevier, vol. 208(2), pages 442-467.
    9. Jingxue Fu & Lan Wu, 2022. "Consistent estimation of the number of regimes in Markov-switching autoregressive models," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 51(8), pages 2496-2518, April.
    10. Stelzer, Robert, 2009. "On Markov-Switching Arma Processes—Stationarity, Existence Of Moments, And Geometric Ergodicity," Econometric Theory, Cambridge University Press, vol. 25(1), pages 43-62, February.
    11. 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.
    12. Maddalena Cavicchioli, 2014. "Determining The Number Of Regimes In Markov Switching Var And Vma Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(2), pages 173-186, March.
    13. Pataracchia, Beatrice, 2011. "The spectral representation of Markov switching ARMA models," Economics Letters, Elsevier, vol. 112(1), pages 11-15, July.
    14. Francq, C. & Zakoian, J. -M., 2001. "Stationarity of multivariate Markov-switching ARMA models," Journal of Econometrics, Elsevier, vol. 102(2), pages 339-364, June.
    15. Hamilton, James D., 1990. "Analysis of time series subject to changes in regime," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 39-70.
    16. Cavicchioli, Maddalena, 2017. "Higher Order Moments Of Markov Switching Varma Models," Econometric Theory, Cambridge University Press, vol. 33(6), pages 1502-1515, December.
    17. Maddalena Cavicchioli, 2014. "Analysis Of The Likelihood Function For Markov-Switching Var(Ch) Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(6), pages 624-639, November.
    18. Nan Li & Simon S. Kwok, 2021. "Jointly determining the state dimension and lag order for Markov‐switching vector autoregressive models," Journal of Time Series Analysis, Wiley Blackwell, vol. 42(4), pages 471-491, July.
    19. Yang, Minxian, 2000. "Some Properties Of Vector Autoregressive Processes With Markov-Switching Coefficients," Econometric Theory, Cambridge University Press, vol. 16(1), pages 23-43, February.
    20. Cavicchioli, Maddalena, 2013. "Spectral density of Markov-switching VARMA models," Economics Letters, Elsevier, vol. 121(2), pages 218-220.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Cavicchioli, Maddalena, 2023. "Statistical analysis of Markov switching vector autoregression models with endogenous explanatory variables," Journal of Multivariate Analysis, Elsevier, vol. 196(C).
    2. Kole, Erik & van Dijk, Dick, 2023. "Moments, shocks and spillovers in Markov-switching VAR models," Journal of Econometrics, Elsevier, vol. 236(2).
    3. Nan Li & Simon S. Kwok, 2021. "Jointly determining the state dimension and lag order for Markov‐switching vector autoregressive models," Journal of Time Series Analysis, Wiley Blackwell, vol. 42(4), pages 471-491, July.
    4. Maddalena Cavicchioli, 2020. "Invertibility and VAR Representations of Time-Varying Dynamic Stochastic General Equilibrium Models," Computational Economics, Springer;Society for Computational Economics, vol. 55(1), pages 61-86, January.
    5. Maddalena Cavicchioli, 2021. "OLS Estimation of Markov switching VAR models: asymptotics and application to energy use," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 105(3), pages 431-449, September.
    6. Cavicchioli, Maddalena, 2013. "Spectral density of Markov-switching VARMA models," Economics Letters, Elsevier, vol. 121(2), pages 218-220.
    7. Fiorentini, Gabriele & Planas, Christophe & Rossi, Alessandro, 2016. "Skewness and kurtosis of multivariate Markov-switching processes," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 153-159.
    8. Maddalena Cavicchioli, 2020. "A note on the asymptotic and exact Fisher information matrices of a Markov switching VARMA process," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 29(1), pages 129-139, March.
    9. Hamilton, J.D., 2016. "Macroeconomic Regimes and Regime Shifts," Handbook of Macroeconomics, in: J. B. Taylor & Harald Uhlig (ed.), Handbook of Macroeconomics, edition 1, volume 2, chapter 0, pages 163-201, Elsevier.
    10. Cavicchioli, Maddalena, 2017. "Asymptotic Fisher information matrix of Markov switching VARMA models," Journal of Multivariate Analysis, Elsevier, vol. 157(C), pages 124-135.
    11. Maddalena Cavicchioli, 2016. "Weak VARMA representations of regime-switching state-space models," Statistical Papers, Springer, vol. 57(3), pages 705-720, September.
    12. Karamé, Frédéric, 2015. "Asymmetries and Markov-switching structural VAR," Journal of Economic Dynamics and Control, Elsevier, vol. 53(C), pages 85-102.
    13. Yacouba Boubacar Maïnassara & Landy Rabehasaina, 2020. "Estimation of weak ARMA models with regime changes," Statistical Inference for Stochastic Processes, Springer, vol. 23(1), pages 1-52, April.
    14. Masaru Chiba, 2023. "Robust and efficient specification tests in Markov-switching autoregressive models," Statistical Inference for Stochastic Processes, Springer, vol. 26(1), pages 99-137, April.
    15. M Boschi & S d'Addona & A Goenka, 2012. "Testing external habits in an asset pricing model," CAMA Working Papers 2012-20, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
    16. Peter Tillmann, 2003. "The Regime‐Dependent Determination of Credibility: A New Look at European Interest Rate Differentials," German Economic Review, Verein für Socialpolitik, vol. 4(4), pages 409-431, November.
    17. Josh Stillwagon & Peter Sullivan, 2020. "Markov switching in exchange rate models: will more regimes help?," Empirical Economics, Springer, vol. 59(1), pages 413-436, July.
    18. Beatrice PATARACCHIA, 2008. "Design-Limits in Regime-Switching cases," EcoMod2008 23800104, EcoMod.
    19. de Bandt,O. & Malik, S., 2010. "Is there Evidence of Shift-Contagion in International Housing Markets?," Working papers 295, Banque de France.
    20. Camacho, Maximo, 2005. "Markov-switching stochastic trends and economic fluctuations," Journal of Economic Dynamics and Control, Elsevier, vol. 29(1-2), pages 135-158, January.

    More about this item

    Keywords

    Markov switching; Vector autoregression; Impulse response function; State-space representation;
    All these keywords.

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ecolet:v:232:y:2023:i:c:s0165176523003828. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/ecolet .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.