IDEAS home Printed from https://ideas.repec.org/a/gam/jecnmx/v7y2019i3p34-d255884.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2225-1146/7/3/34/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2225-1146/7/3/34/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    4. Dimitris N. Politis, 0. "Model-free versus Model-based Volatility Prediction," Journal of Financial Econometrics, Oxford University Press, vol. 5(3), pages 358-359.
    5. 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.
    6. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Kejin Wu & Sayar Karmakar, 2023. "A model-free approach to do long-term volatility forecasting and its variants," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 9(1), pages 1-38, December.
    2. Rangan Gupta & Sayar Karmakar & Christian Pierdzioch, 2024. "Safe Havens, Machine Learning, and the Sources of Geopolitical Risk: A Forecasting Analysis Using Over a Century of Data," Computational Economics, Springer;Society for Computational Economics, vol. 64(1), pages 487-513, July.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Tim Bollerslev, 2008. "Glossary to ARCH (GARCH)," CREATES Research Papers 2008-49, Department of Economics and Business Economics, Aarhus University.
    2. Bali, Turan G. & Weinbaum, David, 2007. "A conditional extreme value volatility estimator based on high-frequency returns," Journal of Economic Dynamics and Control, Elsevier, vol. 31(2), pages 361-397, February.
    3. Dongming Zhu & John W. Galbraith, 2009. "Forecasting Expected Shortfall with a Generalized Asymmetric Student-t Distribution," CIRANO Working Papers 2009s-24, CIRANO.
    4. Abadir, Karim M. & Luati, Alessandra & Paruolo, Paolo, 2023. "GARCH density and functional forecasts," Journal of Econometrics, Elsevier, vol. 235(2), pages 470-483.
    5. Detlef Seese & Christof Weinhardt & Frank Schlottmann (ed.), 2008. "Handbook on Information Technology in Finance," International Handbooks on Information Systems, Springer, number 978-3-540-49487-4, September.
    6. Gatfaoui, Hayette, 2013. "Translating financial integration into correlation risk: A weekly reporting's viewpoint for the volatility behavior of stock markets," Economic Modelling, Elsevier, vol. 30(C), pages 776-791.
    7. Franses,Philip Hans & Dijk,Dick van & Opschoor,Anne, 2014. "Time Series Models for Business and Economic Forecasting," Cambridge Books, Cambridge University Press, number 9780521520911, January.
    8. Alagidede, Paul & Panagiotidis, Theodore, 2009. "Modelling stock returns in Africa's emerging equity markets," International Review of Financial Analysis, Elsevier, vol. 18(1-2), pages 1-11, March.
    9. Kian-Ping Lim & Melvin J. Hinich & Venus Khim-Sen Liew, 2005. "Statistical Inadequacy of GARCH Models for Asian Stock Markets," Journal of Emerging Market Finance, Institute for Financial Management and Research, vol. 4(3), pages 263-279, December.
    10. Eleni Constantinou & Robert Georgiades & Avo Kazandjian & George Kouretas, 2005. "Mean and variance causality between the Cyprus Stock Exchange and major equity markets," Working Papers 0501, University of Crete, Department of Economics.
    11. Brooks, Robert D. & Davidson, Sinclair & Faff, Robert W., 1997. "An examination of the effects of major political change on stock market volatility: the South African experience," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 7(3), pages 255-275, October.
    12. Uctum, Remzi & Renou-Maissant, Patricia & Prat, Georges & Lecarpentier-Moyal, Sylvie, 2017. "Persistence of announcement effects on the intraday volatility of stock returns: Evidence from individual data," Review of Financial Economics, Elsevier, vol. 35(C), pages 43-56.
    13. Mittnik, Stefan & Robinzonov, Nikolay & Spindler, Martin, 2015. "Stock market volatility: Identifying major drivers and the nature of their impact," Journal of Banking & Finance, Elsevier, vol. 58(C), pages 1-14.
    14. McMillan, David G. & Speight, Alan E. H., 2001. "Non-ferrous metals price volatility: a component analysis," Resources Policy, Elsevier, vol. 27(3), pages 199-207, September.
    15. Estrada, Javier, 1995. "Empirical evidence on the impact of European insider trading regulations," DEE - Working Papers. Business Economics. WB 7068, Universidad Carlos III de Madrid. Departamento de Economía de la Empresa.
    16. Yin-Wong Cheung & Frank Westermann, 2001. "Equity Price Dynamics Before and After the Introduction of the Euro: A Note," Multinational Finance Journal, Multinational Finance Journal, vol. 5(2), pages 113-128, June.
    17. Vafiadis Nikolaos, 2015. "Forecasting Volatility and the Risk–Return Tradeoff: An Application on the Fama–French Benchmark Market Return," Journal of Time Series Econometrics, De Gruyter, vol. 7(2), pages 181-216, July.
    18. Michael Pitt & Sheheryar Malik & Arnaud Doucet, 2014. "Simulated likelihood inference for stochastic volatility models using continuous particle filtering," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(3), pages 527-552, June.
    19. Russell, Bill & Chowdhury, Rosen Azad, 2013. "Estimating United States Phillips curves with expectations consistent with the statistical process of inflation," Journal of Macroeconomics, Elsevier, vol. 35(C), pages 24-38.
    20. Mailand, Wilhelm, 1998. "Zum Einfluß von Unsicherheit auf die gesamtwirtschaftliche Investitionstätigkeit," HWWA Discussion Papers 57, Hamburg Institute of International Economics (HWWA).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jecnmx:v:7:y:2019:i:3:p:34-:d:255884. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.