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NoVaS Transformations: Flexible Inference for Volatility Forecasting

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Author Info
Dimitris Politis
Dimitrios Thomakos

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Abstract

In this paper we contribute several new results on the NoVaS transformation approach for volatility forecasting introduced by Politis (2003a,b, 2007). In particular: (a) we introduce an alternative target distribution (uniform); (b) we present a new method for volatility forecasting using NoVaS ; (c) we show that the NoVaS methodology is applicable in situations where (global) stationarity fails such as the cases of local stationarity and/or structural breaks; (d) we show how to apply the NoVaS ideas in the case of returns with asymmetric distribution; and finally (e) we discuss the application of NoVaS to the problem of estimating value at risk (VaR). The NoVaS methodology allows for a flexible approach to inference and has immediate applications in the context of short time series and series that exhibit local behavior (e.g. breaks, regime switching etc.) We conduct an extensive simulation study on the predictive ability of the NoVaS approach and and that NoVaS forecasts lead to a much `tighter' distribution of the forecasting performance measure for all data generating processes. This is especially relevant in the context of volatility predictions for risk management. We further illustrate the use of NoVaS for a number of real datasets and compare the forecasting performance of NoVaS -based volatility forecasts with realized and range-based volatility measures.

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Paper provided by University of Peloponnese, Department of Economics in its series Working Papers with number 0005.

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Length: 67 pages
Date of creation: 2007
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Handle: RePEc:uop:wpaper:0005

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Keywords: ARCH; GARCH; local stationarity; structural breaks; VaR; volatility.;

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  1. 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. [Downloadable!] (restricted)
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  2. Hillebrand, Eric, 2005. "Neglecting parameter changes in GARCH models," Journal of Econometrics, Elsevier, vol. 129(1-2), pages 121-138. [Downloadable!] (restricted)
  3. Parkinson, Michael, 1980. "The Extreme Value Method for Estimating the Variance of the Rate of Return," Journal of Business, University of Chicago Press, vol. 53(1), pages 61-65, January. [Downloadable!] (restricted)
  4. Torben G. Andersen & Tim Bollerslev & Nour Meddahi, 2004. "Analytical Evaluation Of Volatility Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 45(4), pages 1079-1110, November. [Downloadable!] (restricted)
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  5. 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. [Downloadable!]
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  6. Hansen, Peter Reinhard & Lunde, Asger, 2006. "Consistent ranking of volatility models," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 97-121. [Downloadable!] (restricted)
  7. Nour Meddahi, 2001. "An Eigenfunction Approach for Volatility Modeling," CIRANO Working Papers 2001s-70, CIRANO. [Downloadable!]
  8. Cai, Zongwu, 2002. "Regression Quantiles For Time Series," Econometric Theory, Cambridge University Press, vol. 18(01), pages 169-192, February. [Downloadable!]
  9. Meddahi, N., 2001. "An Eigenfunction Approach for Volatility Modeling," Cahiers de recherche 2001-29, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  10. Dimitris Politis, 2004. "A heavy-tailed distribution for ARCH residuals with application to volatility prediction," University of California at San Diego, Economics Working Paper Series 2004-01, Department of Economics, UC San Diego. [Downloadable!]
  11. Hansen, Bruce E., 2006. "Interval forecasts and parameter uncertainty," Journal of Econometrics, Elsevier, vol. 135(1-2), pages 377-398. [Downloadable!] (restricted)
  12. 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.
  13. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2006. "Volatility and Correlation Forecasting," Handbook of Economic Forecasting, Elsevier. [Downloadable!] (restricted)
  14. Liang Peng, 2003. "Least absolute deviations estimation for ARCH and GARCH models," Biometrika, Oxford University Press for Biometrika Trust, vol. 90(4), pages 967-975, December.
  15. Lars Forsberg & Eric Ghysels, 2007. "Why Do Absolute Returns Predict Volatility So Well?," Journal of Financial Econometrics, Oxford University Press, vol. 5(1), pages 31-67. [Downloadable!] (restricted)
  16. MEDDAHI, Nour, 2001. "An Eigenfunction Approach for Volatility Modeling," Cahiers de recherche 2001-29, Universite de Montreal, Departement de sciences economiques. [Downloadable!]
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