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Deriving the autocovariances of powers of Markov-switching GARCH models, with applications to statistical inference

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  • Francq, Christian
  • ZakoI¨an, Jean-Michel

Abstract

A procedure is proposed for computing the autocovariances and the ARMA representations of the squares, and higher-order powers, of Markov-switching GARCH models. It is shown that many interesting subclasses of the general model can be discriminated in view of their autocovariance structures. Explicit derivation of the autocovariances allows for parameter estimation in the general model, via a GMM procedure. It can also be used to determine how many ARMA representations are needed to identify the Markov-switching GARCH parameters. A Monte Carlo study and an application to the Standard & Poor index are presented.

Suggested Citation

  • Francq, Christian & ZakoI¨an, Jean-Michel, 2008. "Deriving the autocovariances of powers of Markov-switching GARCH models, with applications to statistical inference," Computational Statistics & Data Analysis, Elsevier, vol. 52(6), pages 3027-3046, February.
    • Handle: RePEc:eee:csdana:v:52:y:2008:i:6:p:3027-3046
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    1. Carvalho, Carlos M. & Lopes, Hedibert F., 2007. "Simulation-based sequential analysis of Markov switching stochastic volatility models," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4526-4542, May.
    2. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    3. Christian Francq & Michel Roussignol & Jean‐Michel Zakoian, 2001. "Conditional Heteroskedasticity Driven by Hidden Markov Chains," Journal of Time Series Analysis, Wiley Blackwell, vol. 22(2), pages 197-220, March.
    4. Guedon, Yann, 2007. "Exploring the state sequence space for hidden Markov and semi-Markov chains," Computational Statistics & Data Analysis, Elsevier, vol. 51(5), pages 2379-2409, February.
    5. Markus Haas, 2004. "A New Approach to Markov-Switching GARCH Models," Journal of Financial Econometrics, Oxford University Press, vol. 2(4), pages 493-530.
    6. 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.
    7. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    8. Francq, C. & Zakoian, J. -M., 2001. "Stationarity of multivariate Markov-switching ARMA models," Journal of Econometrics, Elsevier, vol. 102(2), pages 339-364, June.
    9. Fong, P.W. & Li, W.K. & An, Hong-Zhi, 2006. "A simple multivariate ARCH model specified by random coefficients," Computational Statistics & Data Analysis, Elsevier, vol. 51(3), pages 1779-1802, December.
    10. Baum, Christopher F & Karasulu, Meral, 1998. "Modelling Federal Reserve Discount Policy," Computational Economics, Springer;Society for Computational Economics, vol. 11(1-2), pages 53-70, April.
    11. Newey, Whitney & West, Kenneth, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 33(1), pages 125-132.
    12. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
    13. Gray, Stephen F., 1996. "Modeling the conditional distribution of interest rates as a regime-switching process," Journal of Financial Economics, Elsevier, vol. 42(1), pages 27-62, September.
    14. Hamilton, James D & Gang, Lin, 1996. "Stock Market Volatility and the Business Cycle," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 11(5), pages 573-593, Sept.-Oct.
    15. Giannikis, D. & Vrontos, I.D. & Dellaportas, P., 2008. "Modelling nonlinearities and heavy tails via threshold normal mixture GARCH models," Computational Statistics & Data Analysis, Elsevier, vol. 52(3), pages 1549-1571, January.
    16. Francq, Christian & ZakoI¨an, Jean-Michel, 2005. "The L2-structures of standard and switching-regime GARCH models," Stochastic Processes and their Applications, Elsevier, vol. 115(9), pages 1557-1582, September.
    17. Cai, Jun, 1994. "A Markov Model of Switching-Regime ARCH," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(3), pages 309-316, July.
    18. Hamilton, James D. & Susmel, Raul, 1994. "Autoregressive conditional heteroskedasticity and changes in regime," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 307-333.
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    Cited by:

    1. Bauwens, Luc & Dufays, Arnaud & Rombouts, Jeroen V.K., 2014. "Marginal likelihood for Markov-switching and change-point GARCH models," Journal of Econometrics, Elsevier, vol. 178(P3), pages 508-522.
    2. Haas Markus, 2010. "Skew-Normal Mixture and Markov-Switching GARCH Processes," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 14(4), pages 1-56, September.
    3. Luc Bauwens & Jean-François Carpantier & Arnaud Dufays, 2017. "Autoregressive Moving Average Infinite Hidden Markov-Switching Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(2), pages 162-182, April.
    4. Billio, Monica & Casarin, Roberto & Osuntuyi, Anthony, 2016. "Efficient Gibbs sampling for Markov switching GARCH models," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 37-57.
    5. Augustyniak, Maciej, 2014. "Maximum likelihood estimation of the Markov-switching GARCH model," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 61-75.
    6. Ataurima Arellano, Miguel & Rodríguez, Gabriel, 2020. "Empirical modeling of high-income and emerging stock and Forex market return volatility using Markov-switching GARCH models," The North American Journal of Economics and Finance, Elsevier, vol. 52(C).
    7. Aknouche, Abdelhakim & Demmouche, Nacer, 2019. "Ergodicity conditions for a double mixed Poisson autoregression," Statistics & Probability Letters, Elsevier, vol. 147(C), pages 6-11.
    8. Thomas Chuffart, 2015. "Selection Criteria in Regime Switching Conditional Volatility Models," Econometrics, MDPI, vol. 3(2), pages 1-28, May.
    9. Gerrit Reher & Bernd Wilfling, 2016. "A nesting framework for Markov-switching GARCH modelling with an application to the German stock market," Quantitative Finance, Taylor & Francis Journals, vol. 16(3), pages 411-426, March.
    10. Aknouche, Abdelhakim & Almohaimeed, Bader & Dimitrakopoulos, Stefanos, 2024. "Noising the GARCH volatility: A random coefficient GARCH model," MPRA Paper 120456, University Library of Munich, Germany, revised 15 Mar 2024.
    11. Abdelhakim Aknouche & Christian Francq, 2022. "Stationarity and ergodicity of Markov switching positive conditional mean models," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(3), pages 436-459, May.
    12. Maciej Augustyniak & Mathieu Boudreault & Manuel Morales, 2018. "Maximum Likelihood Estimation of the Markov-Switching GARCH Model Based on a General Collapsing Procedure," Methodology and Computing in Applied Probability, Springer, vol. 20(1), pages 165-188, March.
    13. Wee, Damien C.H. & Chen, Feng & Dunsmuir, William T.M., 2022. "Likelihood inference for Markov switching GARCH(1,1) models using sequential Monte Carlo," Econometrics and Statistics, Elsevier, vol. 21(C), pages 50-68.
    14. Kai Zheng & Yuying Li & Weidong Xu, 2021. "Regime switching model estimation: spectral clustering hidden Markov model," Annals of Operations Research, Springer, vol. 303(1), pages 297-319, August.
    15. Maddalena Cavicchioli, 2021. "Statistical inference for mixture GARCH models with financial application," Computational Statistics, Springer, vol. 36(4), pages 2615-2642, December.
    16. DUFAYS, Arnaud, 2012. "Infinite-state Markov-switching for dynamic volatility and correlation models," LIDAM Discussion Papers CORE 2012043, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    17. CARPANTIER, Jean-François & DUFAYS, Arnaud, 2014. "Specific Markov-switching behaviour for ARMA parameters," LIDAM Discussion Papers CORE 2014014, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    18. Aknouche, Abdelhakim & Demouche, Nacer, 2018. "Ergodicity conditions for a double mixed Poisson autoregression," MPRA Paper 88843, University Library of Munich, Germany.
    19. Carol Alexander & Emese Lazar, 2009. "Modelling Regime‐Specific Stock Price Volatility," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 71(6), pages 761-797, December.
    20. Hotta, Luiz Koodi & Trucíos Maza, Carlos César & Pereira, Pedro L. Valls & Zevallos Herencia, Mauricio Henrique, 2024. "Forecasting VaR and ES through Markov-switching GARCH models: does the specication matter?," Textos para discussão 567, FGV EESP - Escola de Economia de São Paulo, Fundação Getulio Vargas (Brazil).
    21. Boubacar Mainassara, Y. & Carbon, M. & Francq, C., 2012. "Computing and estimating information matrices of weak ARMA models," Computational Statistics & Data Analysis, Elsevier, vol. 56(2), pages 345-361.
    22. Herrera, Ana María & Hu, Liang & Pastor, Daniel, 2018. "Forecasting crude oil price volatility," International Journal of Forecasting, Elsevier, vol. 34(4), pages 622-635.
    23. Aknouche, Abdelhakim & Demmouche, Nacer & Touche, Nassim, 2018. "Bayesian MCMC analysis of periodic asymmetric power GARCH models," MPRA Paper 91136, University Library of Munich, Germany.
    24. Pérez, Ana & Ruiz, Esther & Veiga, Helena, 2009. "A note on the properties of power-transformed returns in long-memory stochastic volatility models with leverage effect," Computational Statistics & Data Analysis, Elsevier, vol. 53(10), pages 3593-3600, August.
    25. Pappas, Vasileios & Ingham, Hilary & Izzeldin, Marwan & Steele, Gerry, 2016. "Will the crisis “tear us apart”? Evidence from the EU," International Review of Financial Analysis, Elsevier, vol. 46(C), pages 346-360.

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