IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v100y2016icp153-159.html
   My bibliography  Save this article

Skewness and kurtosis of multivariate Markov-switching processes

Author

Listed:
  • Fiorentini, Gabriele
  • Planas, Christophe
  • Rossi, Alessandro

Abstract

Exact formulae are provided for the calculation of multivariate skewness and kurtosis of Markov-switching Vector Auto-Regressive (MS VAR) processes as well as for the general class of MS state space (MS SS) models. The use of the higher-order moments in non-linear modeling is illustrated with two examples. A Matlab code that implements the results is available from the authors.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:100:y:2016:i:c:p:153-159
    DOI: 10.1016/j.csda.2015.06.009
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947315001474
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2015.06.009?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. Cecchetti, Stephen G. & Lam, Pok-sang & Mark, Nelson C., 1993. "The equity premium and the risk-free rate : Matching the moments," Journal of Monetary Economics, Elsevier, vol. 31(1), pages 21-45, February.
    2. Andrew Ang & Allan Timmermann, 2012. "Regime Changes and Financial Markets," Annual Review of Financial Economics, Annual Reviews, vol. 4(1), pages 313-337, October.
    3. Andrew Ang & Geert Bekaert, 2002. "International Asset Allocation With Regime Shifts," The Review of Financial Studies, Society for Financial Studies, vol. 15(4), pages 1137-1187.
    4. Timmermann, Allan, 2000. "Moments of Markov switching models," Journal of Econometrics, Elsevier, vol. 96(1), pages 75-111, May.
    5. Francq, Christian & Zakoïan, Jean-Michel, 2002. "Comments On The Paper By Minxian Yang: “Some Properties Of Vector Autoregressive Processes With Markov-Switching Coefficients”," Econometric Theory, Cambridge University Press, vol. 18(3), pages 815-818, June.
    6. Kollo, Tõnu, 2008. "Multivariate skewness and kurtosis measures with an application in ICA," Journal of Multivariate Analysis, Elsevier, vol. 99(10), pages 2328-2338, November.
    7. Christopher A. Sims & Tao Zha, 2006. "Were There Regime Switches in U.S. Monetary Policy?," American Economic Review, American Economic Association, vol. 96(1), pages 54-81, March.
    8. Farmer, Roger E.A. & Waggoner, Daniel F. & Zha, Tao, 2011. "Minimal state variable solutions to Markov-switching rational expectations models," Journal of Economic Dynamics and Control, Elsevier, vol. 35(12), pages 2150-2166.
    9. Margaret M. McConnell & Gabriel Perez-Quiros, 2000. "Output fluctuations in the United States: what has changed since the early 1980s?," Proceedings, Federal Reserve Bank of San Francisco, issue Mar.
    10. Hess Chung & Troy Davig & Eric M. Leeper, 2007. "Monetary and Fiscal Policy Switching," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 39(4), pages 809-842, June.
    11. Taamouti, Abderrahim, 2012. "Moments of multivariate regime switching with application to risk-return trade-off," Journal of Empirical Finance, Elsevier, vol. 19(2), pages 292-308.
    12. Kim, Chang-Jin, 1993. "Unobserved-Component Time Series Models with Markov-Switching Heteroscedasticity: Changes in Regime and the Link between Inflation Rates and Inflation Uncertainty," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(3), pages 341-349, July.
    13. Troy Davig & Eric M. Leeper, 2007. "Generalizing the Taylor Principle," American Economic Review, American Economic Association, vol. 97(3), pages 607-635, June.
    14. Ang, Andrew & Bekaert, Geert, 2002. "Regime Switches in Interest Rates," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(2), pages 163-182, April.
    15. 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.
    16. Carlo Favero & Tommaso Monacelli, 2005. "Fiscal Policy Rules and Regime (In)Stability: Evidence from the U.S," Working Papers 282, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    17. Chauvet, Marcelle, 1998. "An Econometric Characterization of Business Cycle Dynamics with Factor Structure and Regime Switching," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 969-996, November.
    18. 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.
    19. Francq, C. & Zakoian, J. -M., 2001. "Stationarity of multivariate Markov-switching ARMA models," Journal of Econometrics, Elsevier, vol. 102(2), pages 339-364, June.
    20. Phillips, Kerk L., 1991. "A two-country model of stochastic output with changes in regime," Journal of International Economics, Elsevier, vol. 31(1-2), pages 121-142, August.
    21. Massimo Guidolin & Allan Timmermann, 2005. "Economic Implications of Bull and Bear Regimes in UK Stock and Bond Returns," Economic Journal, Royal Economic Society, vol. 115(500), pages 111-143, January.
    22. Cecchetti, Stephen G & Lam, Pok-sang & Mark, Nelson C, 1990. "Mean Reversion in Equilibrium Asset Prices," American Economic Review, American Economic Association, vol. 80(3), pages 398-418, June.
    23. Farmer, Roger E.A. & Waggoner, Daniel F. & Zha, Tao, 2009. "Understanding Markov-switching rational expectations models," Journal of Economic Theory, Elsevier, vol. 144(5), pages 1849-1867, September.
    24. Chang-Jin Kim & Charles R. Nelson, 1998. "Business Cycle Turning Points, A New Coincident Index, And Tests Of Duration Dependence Based On A Dynamic Factor Model With Regime Switching," The Review of Economics and Statistics, MIT Press, vol. 80(2), pages 188-201, May.
    25. Kim, Chang-Jin, 1994. "Dynamic linear models with Markov-switching," Journal of Econometrics, Elsevier, vol. 60(1-2), pages 1-22.
    26. Maximo Camacho & Gabriel Perez‐Quiros & Pilar Poncela, 2015. "Extracting Nonlinear Signals from Several Economic Indicators," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 30(7), pages 1073-1089, November.
    27. Chang-Jin Kim & Charles R. Nelson, 1999. "Has The U.S. Economy Become More Stable? A Bayesian Approach Based On A Markov-Switching Model Of The Business Cycle," The Review of Economics and Statistics, MIT Press, vol. 81(4), pages 608-616, November.
    28. 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.
    29. Cavicchioli, Maddalena, 2013. "Spectral density of Markov-switching VARMA models," Economics Letters, Elsevier, vol. 121(2), pages 218-220.
    30. Chang-Jin Kim & Charles R. Nelson, 1999. "State-Space Models with Regime Switching: Classical and Gibbs-Sampling Approaches with Applications," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262112388, April.
    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. Zhang, Zhikun & Dai, Min & Wang, Xiangjun, 2023. "Statistical inference for mixed jump processes by Markov switching model with application to identify seismicity levels," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 632(P1).

    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. 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.
    2. Michael T. Owyang & Jeremy Piger & Daniel Soques, 2022. "Contagious switching," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(2), pages 415-432, March.
    3. Magnus Reif, 2020. "Macroeconomics, Nonlinearities, and the Business Cycle," ifo Beiträge zur Wirtschaftsforschung, ifo Institute - Leibniz Institute for Economic Research at the University of Munich, number 87.
    4. Xiaoshan Chen & Ronald Macdonald, 2012. "Realized and Optimal Monetary Policy Rules in an Estimated Markov‐Switching DSGE Model of the United Kingdom," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 44(6), pages 1091-1116, September.
    5. Shaw, Charles, 2018. "Regime-Switching And Levy Jump Dynamics In Option-Adjusted Spreads," MPRA Paper 94154, University Library of Munich, Germany, revised 27 May 2019.
    6. 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.
    7. Andrew Ang & Allan Timmermann, 2012. "Regime Changes and Financial Markets," Annual Review of Financial Economics, Annual Reviews, vol. 4(1), pages 313-337, October.
    8. Baele, Lieven & Bekaert, Geert & Cho, Seonghoon & Inghelbrecht, Koen & Moreno, Antonio, 2015. "Macroeconomic regimes," Journal of Monetary Economics, Elsevier, vol. 70(C), pages 51-71.
    9. Smith, Aaron & Naik, Prasad A. & Tsai, Chih-Ling, 2006. "Markov-switching model selection using Kullback-Leibler divergence," Journal of Econometrics, Elsevier, vol. 134(2), pages 553-577, October.
    10. Cavicchioli, Maddalena, 2023. "Statistical analysis of Markov switching vector autoregression models with endogenous explanatory variables," Journal of Multivariate Analysis, Elsevier, vol. 196(C).
    11. Alexander Karalis Isaac, 2014. "Higher moments of MSVARs and the business cycle," BCAM Working Papers 1405, Birkbeck Centre for Applied Macroeconomics.
    12. Charles Shaw, 2022. "Portfolio Diversification Revisited," Papers 2204.13398, arXiv.org.
    13. Bianchi, Francesco, 2016. "Methods for measuring expectations and uncertainty in Markov-switching models," Journal of Econometrics, Elsevier, vol. 190(1), pages 79-99.
    14. Luke Hartigan, 2015. "Changes in the Factor Structure of the U.S. Economy: Permanent Breaks or Business Cycle Regimes?," Discussion Papers 2015-17, School of Economics, The University of New South Wales.
    15. Zolotoy, Leon & Frederickson, James R. & Lyon, John D., 2017. "Aggregate earnings and stock market returns: The good, the bad, and the state-dependent," Journal of Banking & Finance, Elsevier, vol. 77(C), pages 157-175.
    16. 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.
    17. Konstantin A. Kholodilin, 2006. "Using the Dynamic Bi-Factor Model with Markov Switching to Predict the Cyclical Turns in the Large European Economies," Discussion Papers of DIW Berlin 554, DIW Berlin, German Institute for Economic Research.
    18. Shayan Zakipour-Saber, 2019. "Monetary policy regimes and inflation persistence in the United Kingdom," Working Papers 895, Queen Mary University of London, School of Economics and Finance.
    19. Kole, Erik & van Dijk, Dick, 2023. "Moments, shocks and spillovers in Markov-switching VAR models," Journal of Econometrics, Elsevier, vol. 236(2).
    20. Chevallier, Julien, 2011. "Evaluating the carbon-macroeconomy relationship: Evidence from threshold vector error-correction and Markov-switching VAR models," Economic Modelling, Elsevier, vol. 28(6), pages 2634-2656.

    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:csdana:v:100:y:2016:i:c:p:153-159. 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/csda .

    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.