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Long memory and nonlinearities in realized volatility: a Markov switching approach

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  • S. Bordignon
  • D. Raggi
Abstract
Goal of this paper is to analyze and forecast realized volatility through nonlinear and highly persistent dynamics. In particular, we propose a model that simultaneously captures long memory and nonlinearities in which level and persistence shift through a Markov switching dynamics. We consider an efficient Markov chain Monte Carlo (MCMC) algorithm to estimate parameters, latent process and predictive densities. The insample results show that both long memory and nonlinearities are significant and improve the description of the data. The out-sample results at several forecast horizons, show that introducing these nonlinearities produces superior forecasts over those obtained from nested models.

Suggested Citation

  • S. Bordignon & D. Raggi, 2010. "Long memory and nonlinearities in realized volatility: a Markov switching approach," Working Papers 694, Dipartimento Scienze Economiche, Universita' di Bologna.
    • Handle: RePEc:bol:bodewp:694
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    1. Andersen T. G & Bollerslev T. & Diebold F. X & Labys P., 2001. "The Distribution of Realized Exchange Rate Volatility," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 42-55, March.
    2. 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.
    3. Marcucci Juri, 2005. "Forecasting Stock Market Volatility with Regime-Switching GARCH Models," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 9(4), pages 1-55, December.
    4. McAleer, Michael & Medeiros, Marcelo C., 2008. "A multiple regime smooth transition Heterogeneous Autoregressive model for long memory and asymmetries," Journal of Econometrics, Elsevier, vol. 147(1), pages 104-119, November.
    5. Sangjoon Kim & Neil Shephard & Siddhartha Chib, 1998. "Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 65(3), pages 361-393.
    6. Ohanissian, Arek & Russell, Jeffrey R. & Tsay, Ruey S., 2008. "True or Spurious Long Memory? A New Test," Journal of Business & Economic Statistics, American Statistical Association, vol. 26, pages 161-175, April.
    7. Siem Jan Koopman & Neil Shephard & Jurgen A. Doornik, 1999. "Statistical algorithms for models in state space using SsfPack 2.2," Econometrics Journal, Royal Economic Society, vol. 2(1), pages 107-160.
    8. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2003. "Modeling and Forecasting Realized Volatility," Econometrica, Econometric Society, vol. 71(2), pages 579-625, March.
    9. Michael McAleer & Marcelo Medeiros, 2008. "Realized Volatility: A Review," Econometric Reviews, Taylor & Francis Journals, vol. 27(1-3), pages 10-45.
    10. Baillie, Richard T. & Kapetanios, George, 2007. "Testing for Neglected Nonlinearity in Long-Memory Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 25, pages 447-461, October.
    11. Billio, M. & Monfort, A. & Robert, C. P., 1999. "Bayesian estimation of switching ARMA models," Journal of Econometrics, Elsevier, vol. 93(2), pages 229-255, December.
    12. Federico M. Bandi & Benoit Perron, 2006. "Long Memory and the Relation Between Implied and Realized Volatility," Journal of Financial Econometrics, Oxford University Press, vol. 4(4), pages 636-670.
    13. Koopman, Siem Jan & Jungbacker, Borus & Hol, Eugenie, 2005. "Forecasting daily variability of the S&P 100 stock index using historical, realised and implied volatility measurements," Journal of Empirical Finance, Elsevier, vol. 12(3), pages 445-475, June.
    14. Ole E. Barndorff‐Nielsen & Neil Shephard, 2002. "Econometric analysis of realized volatility and its use in estimating stochastic volatility models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(2), pages 253-280, May.
    15. Susmel, Raul, 2000. "Switching Volatility in Private International Equity Markets," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 5(4), pages 265-283, October.
    16. He, Zhongfang & Maheu, John M., 2010. "Real time detection of structural breaks in GARCH models," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2628-2640, November.
    17. David Ardia, 2009. "Bayesian estimation of a Markov-switching threshold asymmetric GARCH model with Student-t innovations," Econometrics Journal, Royal Economic Society, vol. 12(1), pages 105-126, March.
    18. J. Vermaak & C. Andrieu & A. Doucet & S. J. Godsill, 2004. "Reversible Jump Markov Chain Monte Carlo Strategies for Bayesian Model Selection in Autoregressive Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(6), pages 785-809, November.
    19. Chen, Cathy W.S. & Gerlach, Richard & Lin, Edward M.H., 2008. "Volatility forecasting using threshold heteroskedastic models of the intra-day range," Computational Statistics & Data Analysis, Elsevier, vol. 52(6), pages 2990-3010, February.
    20. Brownlees, C.T. & Gallo, G.M., 2006. "Financial econometric analysis at ultra-high frequency: Data handling concerns," Computational Statistics & Data Analysis, Elsevier, vol. 51(4), pages 2232-2245, December.
    21. Koop, Gary & Ley, Eduardo & Osiewalski, Jacek & Steel, Mark F. J., 1997. "Bayesian analysis of long memory and persistence using ARFIMA models," Journal of Econometrics, Elsevier, vol. 76(1-2), pages 149-169.
    22. Diebold, Francis X & Mariano, Roberto S, 2002. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 134-144, January.
    23. 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.
    24. Diebold, Francis X. & Inoue, Atsushi, 2001. "Long memory and regime switching," Journal of Econometrics, Elsevier, vol. 105(1), pages 131-159, November.
    25. Franc Klaassen, 2002. "Improving GARCH volatility forecasts with regime-switching GARCH," Empirical Economics, Springer, vol. 27(2), pages 363-394.
    26. Dueker, Michael J, 1997. "Markov Switching in GARCH Processes and Mean-Reverting Stock-Market Volatility," Journal of Business & Economic Statistics, American Statistical Association, vol. 15(1), pages 26-34, January.
    27. Granger, Clive W. J. & Ding, Zhuanxin, 1996. "Varieties of long memory models," Journal of Econometrics, Elsevier, vol. 73(1), pages 61-77, July.
    28. Fruhwirth-Schnatter S., 2001. "Markov Chain Monte Carlo Estimation of Classical and Dynamic Switching and Mixture Models," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 194-209, March.
    29. Perron, Pierre & Qu, Zhongjun, 2010. "Long-Memory and Level Shifts in the Volatility of Stock Market Return Indices," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(2), pages 275-290.
    30. Albert, James H & Chib, Siddhartha, 1993. "Bayes Inference via Gibbs Sampling of Autoregressive Time Series Subject to Markov Mean and Variance Shifts," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(1), pages 1-15, January.
    31. Lux, Thomas & Morales-Arias, Leonardo, 2010. "Forecasting volatility under fractality, regime-switching, long memory and student-t innovations," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2676-2692, November.
    32. Ardia, David, 2009. "Bayesian Estimation of the GARCH(1,1) Model with Student-t Innovations in R," MPRA Paper 17414, University Library of Munich, Germany.
    33. Amisano, Gianni & Giacomini, Raffaella, 2007. "Comparing Density Forecasts via Weighted Likelihood Ratio Tests," Journal of Business & Economic Statistics, American Statistical Association, vol. 25, pages 177-190, April.
    34. Fulvio Corsi, 2009. "A Simple Approximate Long-Memory Model of Realized Volatility," Journal of Financial Econometrics, Oxford University Press, vol. 7(2), pages 174-196, Spring.
    35. Eric Hillebrand & Marcelo Cunha Medeiros, 2010. "Asymmetries, breaks, and long-range dependence: An estimation framework for daily realized volatility," Textos para discussão 578, Department of Economics PUC-Rio (Brazil).
    36. Martin Martens & Dick van Dijk & Michiel de Pooter, 2004. "Modeling and Forecasting S&P 500 Volatility: Long Memory, Structural Breaks and Nonlinearity," Tinbergen Institute Discussion Papers 04-067/4, Tinbergen Institute.
    37. Chib, Siddhartha, 1996. "Calculating posterior distributions and modal estimates in Markov mixture models," Journal of Econometrics, Elsevier, vol. 75(1), pages 79-97, November.
    38. Hamilton, James D. & Susmel, Raul, 1994. "Autoregressive conditional heteroskedasticity and changes in regime," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 307-333.
    39. Markus Haas, 2004. "A New Approach to Markov-Switching GARCH Models," Journal of Financial Econometrics, Oxford University Press, vol. 2(4), pages 493-530.
    40. Andersen, Torben G & Bollerslev, Tim, 1998. "Answering the Skeptics: Yes, Standard Volatility Models Do Provide Accurate Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 885-905, November.
    41. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika Van Der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639, October.
    42. Chen, Cathy W.S. & Yu, Tiffany H.K., 2005. "Long-term dependence with asymmetric conditional heteroscedasticity in stock returns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 353(C), pages 413-424.
    43. Longin, Francois M, 1997. "The Threshold Effect in Expected Volatility: A Model Based on Asymmetric Information," The Review of Financial Studies, Society for Financial Studies, vol. 10(3), pages 837-869.
    44. 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.
    45. 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.
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