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Choosing the Best Volatility Models: The Model Confidence Set Approach

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  • Peter Reinhard Hansen
  • Asger Lunde
  • James M. Nason

Abstract

This paper applies the model confidence set (MCS) procedure of Hansen, Lunde and Nason (2003) to a set of volatility models. An MCS is analogous to the confidence interval of a parameter in the sense that it contains the best forecasting model with a certain probability. The key to the MCS is that it acknowledges the limitations of the information in the data. The empirical exercise is based on 55 volatility models and the MCS includes about a third of these when evaluated by mean square error, whereas the MCS contains only a VGARCH model when mean absolute deviation criterion is used. We conduct a simulation study which shows that the MCS captures the superior models across a range of significance levels. When we benchmark the MCS relative to a Bonferroni bound, the latter delivers inferior performance.

Suggested Citation

  • Peter Reinhard Hansen & Asger Lunde & James M. Nason, 2003. "Choosing the Best Volatility Models: The Model Confidence Set Approach," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 65(s1), pages 839-861, December.
    • Handle: RePEc:bla:obuest:v:65:y:2003:i:s1:p:839-861
    DOI: 10.1046/j.0305-9049.2003.00086.x
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    1. Pantula, Sastry G., 1989. "Testing for Unit Roots in Time Series Data," Econometric Theory, Cambridge University Press, vol. 5(2), pages 256-271, August.
    2. Duan, Jin-Chuan, 1997. "Augmented GARCH (p,q) process and its diffusion limit," Journal of Econometrics, Elsevier, vol. 79(1), pages 97-127, July.
    3. Higgins, Matthew L & Bera, Anil K, 1992. "A Class of Nonlinear ARCH Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 33(1), pages 137-158, February.
    4. Asger Lunde & Peter R. Hansen, 2005. "A forecast comparison of volatility models: does anything beat a GARCH(1,1)?," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(7), pages 873-889.
    5. 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.
    6. Clark, Todd E. & McCracken, Michael W., 2001. "Tests of equal forecast accuracy and encompassing for nested models," Journal of Econometrics, Elsevier, vol. 105(1), pages 85-110, November.
    7. Ser-Huang Poon & Clive W.J. Granger, 2003. "Forecasting Volatility in Financial Markets: A Review," Journal of Economic Literature, American Economic Association, vol. 41(2), pages 478-539, June.
    8. Baillie, Richard T. & Bollerslev, Tim & Mikkelsen, Hans Ole, 1996. "Fractionally integrated generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 74(1), pages 3-30, September.
    9. Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, vol. 1(1), pages 83-106, June.
    10. West, Kenneth D, 1996. "Asymptotic Inference about Predictive Ability," Econometrica, Econometric Society, vol. 64(5), pages 1067-1084, September.
    11. Peter Reinhard Hansen, 2001. "An Unbiased and Powerful Test for Superior Predictive Ability," Working Papers 2001-06, Brown University, Department of Economics.
    12. Hansen, Peter Reinhard, 2005. "A Test for Superior Predictive Ability," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 365-380, October.
    13. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    14. 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.
    15. G. William Schwert, 1988. "Why Does Stock Market Volatility Change Over Time?," NBER Working Papers 2798, National Bureau of Economic Research, Inc.
    16. Glosten, Lawrence R & Jagannathan, Ravi & Runkle, David E, 1993. "On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks," Journal of Finance, American Finance Association, vol. 48(5), pages 1779-1801, December.
    17. Peter Hansen, 2003. "Asymptotic Tests of Composite Hypotheses," Working Papers 2003-09, Brown University, Department of Economics.
    18. Barucci, Emilio & Reno, Roberto, 2002. "On measuring volatility of diffusion processes with high frequency data," Economics Letters, Elsevier, vol. 74(3), pages 371-378, February.
    19. Peter Hansen & Asger Lunde, 2003. "Consistent Preordering with an Estimated Criterion Function, with an Application to the Evaluation and Comparison of Volatility Models," Working Papers 2003-01, Brown University, Department of Economics.
    20. Engle, Robert F & Ng, Victor K, 1993. "Measuring and Testing the Impact of News on Volatility," Journal of Finance, American Finance Association, vol. 48(5), pages 1749-1778, December.
    21. Hentschel, Ludger, 1995. "All in the family Nesting symmetric and asymmetric GARCH models," Journal of Financial Economics, Elsevier, vol. 39(1), pages 71-104, September.
    22. West, Kenneth D & McCracken, Michael W, 1998. "Regression-Based Tests of Predictive Ability," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 817-840, November.
    23. Geoffrey F. Loudon & Wing H. Watt & Pradeep K. Yadav, 2000. "An empirical analysis of alternative parametric ARCH models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 15(2), pages 117-136.
    24. Härdle, Wolfgang & Horowitz, Joel L. & Kreiss, Jens-Peter, 2001. "Bootstrap methods for time series," SFB 373 Discussion Papers 2001,59, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    25. Edwin J. Elton, 2002. "Spiders: Where Are the Bugs?," The Journal of Business, University of Chicago Press, vol. 75(3), pages 453-472, July.
    26. Peter Reinhard Hansen & Asger Lunde & James M. Nason, 2005. "Model confidence sets for forecasting models," FRB Atlanta Working Paper 2005-07, Federal Reserve Bank of Atlanta.
    27. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
    28. Enrique Sentana, 1995. "Quadratic ARCH Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 62(4), pages 639-661.
    29. Halbert White, 2000. "A Reality Check for Data Snooping," Econometrica, Econometric Society, vol. 68(5), pages 1097-1126, September.
    30. Johansen, Soren, 1995. "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models," OUP Catalogue, Oxford University Press, number 9780198774501, Decembrie.
    31. Maria Elvira Mancino & Paul Malliavin, 2002. "Fourier series method for measurement of multivariate volatilities," Finance and Stochastics, Springer, vol. 6(1), pages 49-61.
    32. Ole E. Barndorff-Nielsen & Neil Shephard, 2001. "Estimating quadratic variation using realised volatility," Economics Papers 2001-W20, Economics Group, Nuffield College, University of Oxford, revised 01 Nov 2001.
    33. 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.
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