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Model Selection and Testing of Conditional and Stochastic Volatility Models

By M. Caporin and M.J. McAleer


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.asymmetry, leverage;model confidence set;non-nested models;volatility model comparison;volatility model selection;Value-at-Risk forecasts

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  7. (1996). Analytic derivatives and the computation of GARCH estimates,
  8. (1992). ARCH modeling in finance: a review of the theory and empirical evidence,
  9. (1994). ARCH models.
  10. (2000). Asymptotic normality for the quasi-maximum likelihood estimator of a GARCH model, Comptes Rendus de l’Acad´emie des Sciences de Paris, Série I
  11. (2005). Automated inference and learning in modeling financial volatility,
  12. (1982). Autoregressive conditional heteroskedasticity with estimates of the variance of United Kingdom inflation,
  13. (1995). Comparing predictive accuracy,
  14. (1995). Consistance dans les modèles hétéroscedastiques,
  15. (2008). Designing realized kernels to measure the ex post variation of equity prices in the presence of noise,
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  17. (2005). Dynamic asymmetric leverage in stochastic volatility models,
  18. (2002). Econometric analysis of realized volatility and its use in estimating stochastic volatility models,
  19. (2002). Estimating quadratic variation using realized variance,
  20. (2001). Evaluating the predictive accuracy of volatility models,
  21. (2008). Evaluating value-at-risk measures in presence of long memory conditional volatility,
  22. (2009). Evaluating volatility and correlation forecasts,
  23. (1962). Further results on tests of separate families of hypotheses,
  24. (1986). Generalized autoregressive conditional heteroskedasticity,
  25. (2005). Model confidence sets for forecasting models, Federal Reserve Bank of Atlanta WP
  26. (2006). Multivariate stochastic volatility: a review, Econometric Reviews,
  27. (2002). Necessary and sufficient moment conditions for the GARCH(r,s) and asymmetric power GARCH(r,s) models,
  28. (2005). On leverage in a stochastic volatility model,
  29. (2009). On loss functions and ranking forecasting performances of multivariate GARCH models,
  30. (2009). On the efficacy of techniques for evaluating multivariate volatility forecasts,
  31. (1993). On the relation between expected value and the volatility of the nominal excess return on stocks,
  32. (2010). Ranking multivariate GARCH models by problem dimension. Available at SSRN:
  33. (1999). Regulatory evaluation of value-at-risk models,
  34. (1990). Stationarity and persistence in the GARCH (1,1) model,
  35. (2002). Stationarity and the existence of moments of a family of GARCH processes,
  36. (1992). Stationarity of GARCH processes and of some nonnegative time series,
  37. (1996). Statistical aspects of ARCH and stochastic volatility.
  38. (1994). Stochastic volatility in asset prices: estimation with simulated maximum likelihood,
  39. (1998). Stochastic volatility: likelihood inference and comparison with ARCH models,
  40. (1996). Stochastic volatility.
  41. (1995). Techniques for verifying the accuracy of value-at-risk measurement models,
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  43. (2001). The accuracy of density forecasts in risk management,
  44. (1969). The evaluation of economic forecasts,
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