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Computationally efficient bootstrap prediction intervals for returns and volatilities in ARCH and GARCH processes

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  • Bei Chen
  • Yulia R. Gel
  • N. Balakrishna
  • Bovas Abraham

Abstract

We propose a novel, simple, efficient and distribution-free re‐sampling technique for developing prediction intervals for returns and volatilities following ARCH/GARCH models. In particular, our key idea is to employ a Box–Jenkins linear representation of an ARCH/GARCH equation and then to adapt a sieve bootstrap procedure to the nonlinear GARCH framework. Our simulation studies indicate that the new re‐sampling method provides sharp and well calibrated prediction intervals for both returns and volatilities while reducing computational costs by up to 100 times, compared to other available re‐sampling techniques for ARCH/GARCH models. The proposed procedure is illustrated by an application to Yen/U.S. dollar daily exchange rate data. Copyright (C) 2010 John Wiley & Sons, Ltd.

Suggested Citation

  • Bei Chen & Yulia R. Gel & N. Balakrishna & Bovas Abraham, 2011. "Computationally efficient bootstrap prediction intervals for returns and volatilities in ARCH and GARCH processes," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 30(1), pages 51-71, January.
    • Handle: RePEc:jof:jforec:v:30:y:2011:i:1:p:51-71
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    File URL: http://hdl.handle.net/10.1002/for.1197
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    Cited by:

    1. Perera, Indeewara & Silvapulle, Mervyn J., 2021. "Bootstrap based probability forecasting in multiplicative error models," Journal of Econometrics, Elsevier, vol. 221(1), pages 1-24.
    2. Voyant, Cyril & Motte, Fabrice & Notton, Gilles & Fouilloy, Alexis & Nivet, Marie-Laure & Duchaud, Jean-Laurent, 2018. "Prediction intervals for global solar irradiation forecasting using regression trees methods," Renewable Energy, Elsevier, vol. 126(C), pages 332-340.
    3. Beste Hamiye Beyaztas & Ufuk Beyaztas & Soutir Bandyopadhyay & Wei-Min Huang, 2018. "New and Fast Block Bootstrap-Based Prediction Intervals for GARCH(1,1) Process with Application to Exchange Rates," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 80(1), pages 168-194, February.
    4. Zhao, Yuan & Zhang, Weiguo & Gong, Xue & Wang, Chao, 2021. "A novel method for online real-time forecasting of crude oil price," Applied Energy, Elsevier, vol. 303(C).
    5. Ufuk Beyaztas & Beste H. Beyaztas, 2019. "On Jackknife-After-Bootstrap Method for Dependent Data," Computational Economics, Springer;Society for Computational Economics, vol. 53(4), pages 1613-1632, April.
    6. Voyant, Cyril & Notton, Gilles & Darras, Christophe & Fouilloy, Alexis & Motte, Fabrice, 2017. "Uncertainties in global radiation time series forecasting using machine learning: The multilayer perceptron case," Energy, Elsevier, vol. 125(C), pages 248-257.
    7. Trucíos, Carlos & Hotta, Luiz K., 2016. "Bootstrap prediction in univariate volatility models with leverage effect," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 120(C), pages 91-103.

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