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Forecasting returns and volatilities in GARCH processes using the bootstrap

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  • Pascual, Lorenzo

Abstract

We propose a new bootstrap resampling scheme to obtain prediction densities of levels and volatilities of time series generated by GARCH processes. The main advantage over other bootstrap methods previously proposed for GARCH processes, is that the procedure incorpora tes the variability due to parameter estimation and, consequently, it is possible to obtain bootstrap prediction densities for the volatility process. The asymptotic properties of the procedure are derived and the finite sample properties are analysed by means of Monte CarIo experiments, showing its good behaviour versus altemative procedures. Finally, the procedure is applied to estimate prediction densities of retums and volatilities of the Madrid Stock Market index, IBEX-35.

Suggested Citation

  • Pascual, Lorenzo, 2000. "Forecasting returns and volatilities in GARCH processes using the bootstrap," DES - Working Papers. Statistics and Econometrics. WS 10059, Universidad Carlos III de Madrid. Departamento de Estadística.
    • Handle: RePEc:cte:wsrepe:10059
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    References listed on IDEAS

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    1. Jesús Miguel & Pilar Olave, 1999. "Bootstrapping forecast intervals in ARCH models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 8(2), pages 345-364, December.
    2. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 1999. "The Distribution of Exchange Rate Volatility," Center for Financial Institutions Working Papers 99-08, Wharton School Center for Financial Institutions, University of Pennsylvania.
    3. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    4. Andersen, Torben G, 2000. "Some Reflections on Analysis of High-Frequency Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(2), pages 146-153, April.
    5. Andrew Harvey & Esther Ruiz & Neil Shephard, 1994. "Multivariate Stochastic Variance Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 61(2), pages 247-264.
    6. Bollerslev, Tim, 1987. "A Conditionally Heteroskedastic Time Series Model for Speculative Prices and Rates of Return," The Review of Economics and Statistics, MIT Press, vol. 69(3), pages 542-547, August.
    7. Baillie, Richard T. & Bollerslev, Tim, 1992. "Prediction in dynamic models with time-dependent conditional variances," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 91-113.
    8. Andersen, Torben G & Bollerslev, Tim, 1998. "Answering the Skeptics: Yes, Standard Volatility Models Do Provide Accurate Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 885-905, November.
    9. 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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    Cited by:

    1. Marinho G. Andrade & Sandra C. Oliveira, 2011. "A Comparative Study Of Bayesian And Maximum Likelihood Approaches For Arch Models With Evidence From Brazilian Financial Series," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 7(02), pages 347-361.

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