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Optimal Multi-Step-Ahead Prediction of ARCH/GARCH Models and NoVaS Transformation

Author

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  • Jie Chen

    (Department of Mathematics, University of California, San Diego, CA 92093, USA)

  • Dimitris N. Politis

    (Department of Mathematics, University of California, San Diego, CA 92093, USA)

Abstract

This paper gives a computer-intensive approach to multi-step-ahead prediction of volatility in financial returns series under an ARCH/GARCH model and also under a model-free setting, namely employing the NoVaS transformation. Our model-based approach only assumes i . i . d innovations without requiring knowledge/assumption of the error distribution and is computationally straightforward. The model-free approach is formally quite similar, albeit a GARCH model is not assumed. We conducted a number of simulations to show that the proposed approach works well for both point prediction (under L 1 and/or L 2 measures) and prediction intervals that were constructed using bootstrapping. The performance of GARCH models and the model-free approach for multi-step ahead prediction was also compared under different data generating processes.

Suggested Citation

  • Jie Chen & Dimitris N. Politis, 2019. "Optimal Multi-Step-Ahead Prediction of ARCH/GARCH Models and NoVaS Transformation," Econometrics, MDPI, vol. 7(3), pages 1-23, August.
    • Handle: RePEc:gam:jecnmx:v:7:y:2019:i:3:p:34-:d:255884
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    References listed on IDEAS

    as
    1. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2006. "Volatility and Correlation Forecasting," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 1, chapter 15, pages 777-878, Elsevier.
    2. Bollerslev, Tim & Chou, Ray Y. & Kroner, Kenneth F., 1992. "ARCH modeling in finance : A review of the theory and empirical evidence," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 5-59.
    3. Dimitris N. Politis, 0. "Model-free versus Model-based Volatility Prediction," Journal of Financial Econometrics, Oxford University Press, vol. 5(3), pages 358-359.
    4. 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.
    5. Pan, Li & Politis, Dimitris, 2014. "Bootstrap prediction intervals for Markov processes," University of California at San Diego, Economics Working Paper Series qt7555757g, Department of Economics, UC San Diego.
    6. Arup Bose & Kanchan Mukherjee, 2009. "Bootstrapping a weighted linear estimator of the ARCH parameters," Journal of Time Series Analysis, Wiley Blackwell, vol. 30(3), pages 315-331, May.
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    Cited by:

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    2. Rangan Gupta & Sayar Karmakar & Christian Pierdzioch, 2022. "Safe Havens, Machine Learning, and the Sources of Geopolitical Risk: A Forecasting Analysis Using Over a Century of Data," Working Papers 202201, University of Pretoria, Department of Economics.

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