IDEAS home Printed from https://ideas.repec.org/a/bla/jtsera/v35y2014i6p624-639.html
   My bibliography  Save this article

Analysis Of The Likelihood Function For Markov-Switching Var(Ch) Models

Author

Listed:
  • Maddalena Cavicchioli

Abstract

type="main" xml:id="jtsa12085-abs-0001"> In this work, we give simple matrix formulae for maximum likelihood estimates of parameters in a broad class of vector autoregressions subject to Markovian changes in regime. This allows us to determine explicitly the asymptotic variance–covariance matrix of the estimators, giving a concrete possibility for the use of the classical testing procedures. In the context of multivariate autoregressive conditional heteroskedastic models with changes in regime, we provide formulae for the analytic derivatives of the log likelihood. Then we prove the consistency of some maximum likelihood estimators and give some formulae for the asymptotic variance of the different estimators.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:jtsera:v:35:y:2014:i:6:p:624-639
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1111/jtsa.12085
    Download Restriction: Access to full text is restricted to subscribers.
    ---><---

    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. Francq, C. & Zakoian, J. -M., 2001. "Stationarity of multivariate Markov-switching ARMA models," Journal of Econometrics, Elsevier, vol. 102(2), pages 339-364, June.
    2. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, vol. 11(1), pages 122-150, February.
    3. Weiss, Andrew A., 1986. "Asymptotic Theory for ARCH Models: Estimation and Testing," Econometric Theory, Cambridge University Press, vol. 2(1), pages 107-131, April.
    4. Kim, Chang-Jin, 1994. "Dynamic linear models with Markov-switching," Journal of Econometrics, Elsevier, vol. 60(1-2), pages 1-22.
    5. Hamilton, James D., 1990. "Analysis of time series subject to changes in regime," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 39-70.
    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. Cavicchioli, Maddalena, 2023. "Statistical analysis of Markov switching vector autoregression models with endogenous explanatory variables," Journal of Multivariate Analysis, Elsevier, vol. 196(C).
    2. Cavicchioli, Maddalena, 2017. "Asymptotic Fisher information matrix of Markov switching VARMA models," Journal of Multivariate Analysis, Elsevier, vol. 157(C), pages 124-135.
    3. 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.
    4. Kangogo, Moses & Volkov, Vladimir, 2022. "Detecting signed spillovers in global financial markets: A Markov-switching approach," International Review of Financial Analysis, Elsevier, vol. 82(C).
    5. BenSaïda, Ahmed & Litimi, Houda & Abdallah, Oussama, 2018. "Volatility spillover shifts in global financial markets," Economic Modelling, Elsevier, vol. 73(C), pages 343-353.
    6. 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.
    7. 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.

    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. Tom A. FEARNLEY, 2002. "Tests of an International Capital Asset Pricing Model with Stocks and Government Bonds and Regime Switching Prices of Risk and Intercepts," FAME Research Paper Series rp97, International Center for Financial Asset Management and Engineering.
    2. Tom A. FEARNLEY, 2002. "Estimation of an International Capital Asset Pricing Model with Stocks and Government Bonds," FAME Research Paper Series rp95, International Center for Financial Asset Management and Engineering.
    3. Cavicchioli, Maddalena, 2017. "Asymptotic Fisher information matrix of Markov switching VARMA models," Journal of Multivariate Analysis, Elsevier, vol. 157(C), pages 124-135.
    4. Maddalena Cavicchioli, 2016. "Weak VARMA representations of regime-switching state-space models," Statistical Papers, Springer, vol. 57(3), pages 705-720, September.
    5. Giampiero Gallo & Edoardo Otranto, 2006. "Volatility Transmission Across Markets: A Multi-Chain Markov Switching Model," Econometrics Working Papers Archive wp2006_04, Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti".
    6. Kole, Erik & van Dijk, Dick, 2023. "Moments, shocks and spillovers in Markov-switching VAR models," Journal of Econometrics, Elsevier, vol. 236(2).
    7. Dominique Guegan & Bertrand K. Hassani, 2019. "Risk Measurement," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-02119256, HAL.
    8. Oscar V. De la Torre-Torres & Evaristo Galeana-Figueroa & María de la Cruz Del Río-Rama & José Álvarez-García, 2022. "Using Markov-Switching Models in US Stocks Optimal Portfolio Selection in a Black–Litterman Context (Part 1)," Mathematics, MDPI, vol. 10(8), pages 1-28, April.
    9. 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.
    10. LeBaron, Blake, 2003. "Non-Linear Time Series Models in Empirical Finance,: Philip Hans Franses and Dick van Dijk, Cambridge University Press, Cambridge, 2000, 296 pp., Paperback, ISBN 0-521-77965-0, $33, [UK pound]22.95, [," International Journal of Forecasting, Elsevier, vol. 19(4), pages 751-752.
    11. Franses,Philip Hans & Dijk,Dick van, 2000. "Non-Linear Time Series Models in Empirical Finance," Cambridge Books, Cambridge University Press, number 9780521779654.
    12. Jean Marcelin B. Brou & Mbodja Mougoué & Eugene Kouassi & Kebaabetswe Thulaganyo & Benjamin K. Acquah, 2022. "Effects of diamond price volatility on stock returns: Evidence from a developing economy," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 27(1), pages 1025-1043, January.
    13. 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.
    14. Shively, Gerald E., 2001. "Price thresholds, price volatility, and the private costs of investment in a developing country grain market," Economic Modelling, Elsevier, vol. 18(3), pages 399-414, August.
    15. Moerman, G.A., 2001. "Unpredictable After All? A short note on exchange rate predictability," ERIM Report Series Research in Management ERS-2001-29-F&A, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    16. Yip, Pick Schen & Brooks, Robert & Do, Hung Xuan & Nguyen, Duc Khuong, 2020. "Dynamic volatility spillover effects between oil and agricultural products," International Review of Financial Analysis, Elsevier, vol. 69(C).
    17. Vassilios Babalos & Mehmet Balcilar & Rangan Gupta, 2014. "Revisiting Herding Behavior in REITs: A Regime-Switching Approach," Working Papers 201448, University of Pretoria, Department of Economics.
    18. Theobald, Thomas, 2013. "Markov Switching with Endogenous Number of Regimes and Leading Indicators in a Real-Time Business Cycle Forecast," VfS Annual Conference 2013 (Duesseldorf): Competition Policy and Regulation in a Global Economic Order 79911, Verein für Socialpolitik / German Economic Association.
    19. Dmitry Kulikov, 2012. "Testing for Rational Speculative Bubbles on the Estonian Stock Market," Research in Economics and Business: Central and Eastern Europe, Tallinn School of Economics and Business Administration, Tallinn University of Technology, vol. 4(1).
    20. Sucarrat, Genaro & Grønneberg, Steffen & Escribano, Alvaro, 2016. "Estimation and inference in univariate and multivariate log-GARCH-X models when the conditional density is unknown," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 582-594.

    More about this item

    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:bla:jtsera:v:35:y:2014:i:6:p:624-639. 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: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0143-9782 .

    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.