IDEAS home Printed from https://ideas.repec.org/a/psc/journl/v6y2014i4p275-289.html
   My bibliography  Save this article

Autocovariance and Linear Transformations of Markov Switching VARMA Processes

Author

Listed:
  • Maddalena Cavicchioli

    (University of Modena and Reggio Emilia)

Abstract

We study the autocovariance structure of a general Markov switching second-order stationary VARMA model. Then we give stable finite order VARMA(p*, q*) representations for those M-state Markov switching VARMA(p, q) processes where the observables are uncorrelated with the regime variables. This allows us to obtain sharper bounds for p* and q* with respect to the ones existing in literature. Our results provide new insights into stochastic properties and facilitate statistical inference about the orders of MS-VARMA models and the underlying number of hidden states.

Suggested Citation

  • Maddalena Cavicchioli, 2014. "Autocovariance and Linear Transformations of Markov Switching VARMA Processes," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 6(4), pages 275-289, December.
    • Handle: RePEc:psc:journl:v:6:y:2014:i:4:p:275-289
    as

    Download full text from publisher

    File URL: http://www.cejeme.eu/publishedarticles/2014-41-24-635550504616093750-1290.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. Massimo Guidolin, 2011. "Markov Switching Models in Empirical Finance," Advances in Econometrics, in: Missing Data Methods: Time-Series Methods and Applications, pages 1-86, Emerald Group Publishing Limited.
    3. 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.
    4. Bergman, U. Michael & Hansson, Jesper, 2005. "Real exchange rates and switching regimes," Journal of International Money and Finance, Elsevier, vol. 24(1), pages 121-138, February.
    5. Dumas, Bernard, 1992. "Dynamic Equilibrium and the Real Exchange Rate in a Spatially Separated World," The Review of Financial Studies, Society for Financial Studies, vol. 5(2), pages 153-180.
    6. Zacharias Psaradakis & Nicola Spagnolo, 2003. "On The Determination Of The Number Of Regimes In Markov‐Switching Autoregressive Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(2), pages 237-252, March.
    7. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.

    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, 2024. "A matrix unified framework for deriving various impulse responses in Markov switching VAR: Evidence from oil and gas markets," The Journal of Economic Asymmetries, Elsevier, vol. 29(C).
    2. 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.
    3. Kole, Erik & van Dijk, Dick, 2023. "Moments, shocks and spillovers in Markov-switching VAR models," Journal of Econometrics, Elsevier, vol. 236(2).
    4. Cavicchioli, Maddalena, 2023. "Impulse response function analysis for Markov switching var models," Economics Letters, Elsevier, vol. 232(C).
    5. Cavicchioli, Maddalena, 2023. "Statistical analysis of Markov switching vector autoregression models with endogenous explanatory variables," Journal of Multivariate Analysis, Elsevier, vol. 196(C).
    6. Maddalena Cavicchioli, 2016. "Weak VARMA representations of regime-switching state-space models," Statistical Papers, Springer, vol. 57(3), pages 705-720, September.
    7. Lee, Hwa-Taek & Yoon, Gawon, 2007. "Does Purchasing Power Parity Hold Sometimes? Regime Switching in Real Exchange Rates," Economics Working Papers 2007-24, Christian-Albrechts-University of Kiel, Department of Economics.
    8. 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.
    9. Zied Ftiti & Slim Chaouachi, 2018. "What Can We Learn About the Real Exchange Rate Behavior in the Case of a Peripheral Country?," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 16(3), pages 681-707, September.
    10. Maddalena Cavicchioli, 2015. "Likelihood Ratio Test and Information Criteria for Markov Switching Var Models: An Application to the Italian Macroeconomy," Italian Economic Journal: A Continuation of Rivista Italiana degli Economisti and Giornale degli Economisti, Springer;Società Italiana degli Economisti (Italian Economic Association), vol. 1(3), pages 315-332, November.
    11. Hwa-Taek Lee & Gawon Yoon, 2013. "Does purchasing power parity hold sometimes? Regime switching in real exchange rates," Applied Economics, Taylor & Francis Journals, vol. 45(16), pages 2279-2294, June.
    12. Daniel Aromi & Marcos Dal Bianco, 2014. "Un analisis de los desequilibrios del tipo de cambio real argentino bajo cambios de regimen," Working Papers 1431, BBVA Bank, Economic Research Department.
    13. Marie-Christine Duker & David S. Matteson & Ruey S. Tsay & Ines Wilms, 2024. "Vector AutoRegressive Moving Average Models: A Review," Papers 2406.19702, arXiv.org.
    14. Basher, Syed Abul & Haug, Alfred A. & Sadorsky, Perry, 2016. "The impact of oil shocks on exchange rates: A Markov-switching approach," Energy Economics, Elsevier, vol. 54(C), pages 11-23.
    15. Constandina Koki & Stefanos Leonardos & Georgios Piliouras, 2020. "Exploring the Predictability of Cryptocurrencies via Bayesian Hidden Markov Models," Papers 2011.03741, arXiv.org, revised Dec 2020.
    16. Frédérique Bec & Mélika Ben Salem & Ronald MacDonald, 2006. "Real exchange rates and real interest rates : a nonlinear perspective," Recherches économiques de Louvain, De Boeck Université, vol. 72(2), pages 177-194.
    17. Maddalena Cavicchioli, 2013. "�Determining the Number of Regimes in Markov-Switching VAR and VMA Models�," Working Papers 2013:03, Department of Economics, University of Venice "Ca' Foscari".
    18. Aloy, Marcel & Boutahar, Mohamed & Gente, Karine & Péguin-Feissolle, Anne, 2011. "Purchasing power parity and the long memory properties of real exchange rates: Does one size fit all?," Economic Modelling, Elsevier, vol. 28(3), pages 1279-1290, May.
    19. 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.
    20. Koki, Constandina & Leonardos, Stefanos & Piliouras, Georgios, 2022. "Exploring the predictability of cryptocurrencies via Bayesian hidden Markov models," Research in International Business and Finance, Elsevier, vol. 59(C).

    More about this item

    Keywords

    time series; multivariate ARMA; state-space models; Markov chains; changes in regime; autocovariance; linear representations;
    All these keywords.

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • 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

    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:psc:journl:v:6:y:2014:i:4:p:275-289. 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: Damian Jelito (email available below). General contact details of provider: http://cejeme.org/ .

    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.