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Model Selection and Testing of Conditional and Stochastic Volatility Models

This paper focuses on the selection and comparison of alternative non-nested volatility models. We review the traditional in-sample methods commonly applied in the volatility framework, namely diagnostic checking procedures, information criteria, and conditions for the existence of moments and asymptotic theory, as well as the out-of-sample model selection approaches, such as mean squared error and Model Confidence Set approaches. The paper develops some innovative loss functions which are based on Value-at-Risk forecasts. Finally, we present an empirical application based on simple univariate volatility models, namely GARCH, GJR, EGARCH, and Stochastic Volatility that are widely used to capture asymmetry and leverage.

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Paper provided by University of Canterbury, Department of Economics and Finance in its series Working Papers in Economics with number 10/58.

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Length: 31 pages
Date of creation: 01 Sep 2010
Date of revision:
Handle: RePEc:cbt:econwp:10/58
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  1. McAleer, Michael, 2005. "Automated Inference And Learning In Modeling Financial Volatility," Econometric Theory, Cambridge University Press, vol. 21(01), pages 232-261, February.
  2. Masahito Kobayashi & Xiuhong Shi, 2005. "Testing for EGARCH Against Stochastic Volatility Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(1), pages 135-150, 01.
  3. Jun Yu, 2004. "On leverage in a stochastic volatility model," Econometric Society 2004 Far Eastern Meetings 497, Econometric Society.
  4. Ole E. Barndorff-Nielsen & 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.
  5. Shiqing Ling & Michael McAleer, 2001. "Stationarity and the Existence of Moments of a Family of GARCH Processes," ISER Discussion Paper 0535, Institute of Social and Economic Research, Osaka University.
  6. Jung-Hee Lee & B. Wade Brorsen, 1997. "A non-nested test of GARCH vs. EGARCH models," Applied Economics Letters, Taylor & Francis Journals, vol. 4(12), pages 765-768.
  7. Sangjoon Kim & Neil Shephard & Siddhartha Chib, 1998. "Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models," Review of Economic Studies, Oxford University Press, vol. 65(3), pages 361-393.
  8. Massimiliano Caporin & Michael McAleer, 2010. "Ranking Multivariate GARCH Models by Problem Dimension," CARF F-Series CARF-F-219, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
  9. Manabu Asai & Michael McAleer & Jun Yu, 2006. "Multivariate Stochastic Volatility: A Review," Econometric Reviews, Taylor & Francis Journals, vol. 25(2-3), pages 145-175.
  10. Neil Shephard & Ole E. Barndorff-Nielsen, 2006. "Designing realised kernels to measure the ex-post variation of equity prices in the presence of noise," Economics Series Working Papers 2006-W03, University of Oxford, Department of Economics.
  11. Bougerol, Philippe & Picard, Nico, 1992. "Stationarity of Garch processes and of some nonnegative time series," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 115-127.
  12. Neil Shephard & Ole E. Barndorff-Nielsen, 2002. "Estimating quadratic variation using realised variance," Economics Series Working Papers 2001-W20, University of Oxford, Department of Economics.
  13. Danielsson, Jon, 1994. "Stochastic volatility in asset prices estimation with simulated maximum likelihood," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 375-400.
  14. Jacob A. Mincer & Victor Zarnowitz, 1969. "The Evaluation of Economic Forecasts," NBER Chapters, in: Economic Forecasts and Expectations: Analysis of Forecasting Behavior and Performance, pages 3-46 National Bureau of Economic Research, Inc.
  15. Massimiliano Caporin & Michael McAleer, 2009. "Do We Really Need Both BEKK and DCC? A Tale of Two Covariance Models," Documentos de Trabajo del ICAE 0904, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
  16. Sébastien Laurent & Jeroen Rombouts & Francesco Violente, 2009. "On Loss Functions and Ranking Forecasting Performances of Multivariate Volatility Models," CIRANO Working Papers 2009s-45, CIRANO.
  17. Ling, Shiqing & McAleer, Michael, 2002. "NECESSARY AND SUFFICIENT MOMENT CONDITIONS FOR THE GARCH(r,s) AND ASYMMETRIC POWER GARCH(r,s) MODELS," Econometric Theory, Cambridge University Press, vol. 18(03), pages 722-729, June.
  18. Diebold, Francis X & Mariano, Roberto S, 1995. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(3), pages 253-63, July.
  19. Jose A. Lopez, 1995. "Evaluating the predictive accuracy of volatility models," Research Paper 9524, Federal Reserve Bank of New York.
  20. Bollerslev, Tim & Chou, Ray Y. & Kroner, Kenneth F., 1992. "ARCH modeling in finance : A review of the theory and empirical evidence," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 5-59.
  21. McAleer, Michael & Chan, Felix & Marinova, Dora, 2007. "An econometric analysis of asymmetric volatility: Theory and application to patents," Journal of Econometrics, Elsevier, vol. 139(2), pages 259-284, August.
  22. Nelson, Daniel B., 1990. "Stationarity and Persistence in the GARCH(1,1) Model," Econometric Theory, Cambridge University Press, vol. 6(03), pages 318-334, September.
  23. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
  24. Hansen, Peter Reinhard, 2005. "A Test for Superior Predictive Ability," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 365-380, October.
  25. 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.
  26. Manabu Asai & Michael McAleer, 2005. "Dynamic Asymmetric Leverage in Stochastic Volatility Models," Econometric Reviews, Taylor & Francis Journals, vol. 24(3), pages 317-332.
  27. So, Mike K P & Li, W K & Lam, K, 2002. "A Threshold Stochastic Volatility Model," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 21(7), pages 473-500, November.
  28. Fiorentini, Gabriele & Calzolari, Giorgio & Panattoni, Lorenzo, 1996. "Analytic Derivatives and the Computation of GARCH Estimates," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 11(4), pages 399-417, July-Aug..
  29. Sangjoon Kim & Neil Shephard & Siddhartha Chib, 1998. "Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models," Review of Economic Studies, Oxford University Press, vol. 65(3), pages 361-393.
  30. Adam Clements & Mark Doolan & Stan Hurn & Ralf Becker, 2009. "Evaluating multivariate volatility forecasts," NCER Working Paper Series 41, National Centre for Econometric Research, revised 25 Nov 2009.
  31. Halbert White, 2000. "A Reality Check for Data Snooping," Econometrica, Econometric Society, vol. 68(5), pages 1097-1126, September.
  32. 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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