Evaluating the performance of GARCH models using White´s Reality Check (original) (raw)

2002, Textos para discussão

Abstract

The important issue of forecasting volatilities brings en suite the difficult task of backtesting the forecasting performance. As the volatility cannot be observed directly, one has to use a observable proxy for the volatility or a utility function to assess the prediction quality. This kind of procedure can easily lead to a poor assessment. The goal of this paper is to compare different volatility models and different performance measures using White´s Reality Check. The Reality Check consists of a non-parametric test that checks if any of a number of concurrent methods yields forecasts significantly better than a given benchmark method. For this purpose, a Monte Carlo simulation is carried out with four different processes, one of them a Gaussian white noise and the others following GARCH specifications. Two benchmark methods are used: the naive (predicting the out-of-sample volatility by the in sample variance) and the Riskmetrics method.

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References (20)

  1. Andersen, T., and T. Bollerslev (1998): "Answering the Skeptics: Yes, Standard Volatility Models Do Provide Accurate Forecasts," International Economic Review, 39, 885-906.
  2. Bollerslev, T. (1986): "Generalized Autoregressive Conditional Heteroskedasticity," Journal of Econometrics, 21, 307-328.
  3. Bollerslev, T., R. F. Engle, and D. B. Nelson (1994): "ARCH Models," in Handbook of Econometrics, ed. by R. F. Engle, and D. McFadden, vol. 4, pp. 2959-3038. North Holland.
  4. Bollerslev, T., and E. Ghysels (1996): "Periodic Autoregressive Conditional Heteroskedas- ticity," Journal of Business and Economic Statistics, 14, 139-157.
  5. Brooks, C., S. P. Burke, and G. Persand (2001): "Benchmarks and the Accuracy of GARCH Model Estimation," International Journal of Forecasting, 17, 45-56.
  6. Clements, M., and J. Smith (1997): "The Performance of Alternative Forecasting Methods for SETAR Models," International Journal of Forecasting, 13, 463-475.
  7. Cumby, R., S. Figlewski, and J. Hasbrouck (1993): "Forecasting Volatility and Correlations with EGARCH Models," Journal of Derivatives, Winter, 51-63.
  8. Engle, R. F. (1982): "Autoregressive Conditional Heteroskedasticity with Estimates of the Vari- ance of UK Inflations," Econometrica, 50, 987-1007.
  9. Figlewski, S. (1997): "Forecasting Volatility," Financial Markets, Institutions, and Instruments, 6, 1-88.
  10. Hansen, P. R. (2001): "A Test for Superior Predictive Ability," Department of Economics Work- ing Paper in Economics 01-06, Brown University.
  11. Hansen, P. R., and A. Lunde (2001): "A Forecast Comparison of Volatility Models: Does Anything beat a GARCH(1,1) Model?," Journal of Applied Econometrics, forthcoming. (2003): "Consistent Ranking of Volatility Models," Journal of Econometrics, forthcoming.
  12. He, C., and T. Teräsvirta (1999a): "Properties of moments of a family of GARCH processes," Journal of Econometrics, 92, 173-192. (1999b): "Properties of the autocorrelation function of squared observations for second order GARCH processes under two sets of parameter constraints," Journal of Time Series Anal- ysis, 20, 23-30.
  13. Jorion, P. (1995): "Predicting Volatility in the Foreign Exchange Market," Journal of Finance, 50, 507-528. (1996): "Risk and Turnover in the Foreign Exchange Market," in The Microstructure of Foreign Exchange Markets, ed. by J. A. Frankel, G. Galli, and A. Giovanni, pp. 19-37. University of Chicago Press.
  14. Lopez, J. A. (2001): "Evaluating the Predictive Accuracy of Volatility Models," Journal of Fore- casting, 20, 87-109.
  15. Lundbergh, S., and T. Teräsvirta (2002): "Forecasting with Smooth Transition Autoregressive Models," in A Companion to Economic Forecasting, ed. by M. P. Clements, and D. F. Hendry, pp. 485-509. Oxford: Blackwell.
  16. Malmsten, H., and T. Teräsvirta (2004): "Stylized Facts of Financial Time Series and Three Popular Models of Volatility," Working Paper Series in Economics and Finance 563, Stockholm School of Economics.
  17. Morgan, J. P. (1996): J. P. Morgan/Reuters Riskmetrics -Technical Document. J. P. Morgan, New York.
  18. Pagan, A. R., and G. W. Schwert (1990): "Alternative Models for Conditional Stock Volatil- ity," Journal of Econometrics, 45, 267-290.
  19. Politis, D., and J. Romano (1994): "The Stationary Bootstrap," Journal of the American Statistical Association, 89, 1303-1313.
  20. Teräsvirta, T. (1996): "Two Stylized Facts and the GARCH(1,1) Model," Working Paper Series in Economics and Finance 96, Stockholm School of Economics.