IDEAS home Printed from https://ideas.repec.org/a/eee/empfin/v38y2016ipbp534-547.html
   My bibliography  Save this article

Strict stationarity, persistence and volatility forecasting in ARCH(∞) processes

Author

Listed:
  • Davidson, James
  • Li, Xiaoyu

Abstract

This paper derives a simple sufficient condition for strict stationarity in the ARCH(∞) class of processes with conditional heteroscedasticity. The concept of persistence in these processes is explored, and is the subject of a set of simulations showing how persistence depends on both the pattern of lag coefficients of the ARCH model and the distribution of the driving shocks. The results are used to argue that an alternative to the usual method of ARCH/GARCH volatility forecasting should be considered.

Suggested Citation

  • Davidson, James & Li, Xiaoyu, 2016. "Strict stationarity, persistence and volatility forecasting in ARCH(∞) processes," Journal of Empirical Finance, Elsevier, vol. 38(PB), pages 534-547.
    • Handle: RePEc:eee:empfin:v:38:y:2016:i:pb:p:534-547
    DOI: 10.1016/j.jempfin.2015.08.010
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0927539815000948
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jempfin.2015.08.010?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Davidson, James, 1994. "Stochastic Limit Theory: An Introduction for Econometricians," OUP Catalogue, Oxford University Press, number 9780198774037.
    2. Douc, Randal & Roueff, François & Soulier, Philippe, 2008. "On the existence of some processes," Stochastic Processes and their Applications, Elsevier, vol. 118(5), pages 755-761, May.
    3. Thomas Mikosch & Cătălin Stărică, 2004. "Nonstationarities in Financial Time Series, the Long-Range Dependence, and the IGARCH Effects," The Review of Economics and Statistics, MIT Press, vol. 86(1), pages 378-390, February.
    4. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    5. Beveridge, Stephen & Nelson, Charles R., 1981. "A new approach to decomposition of economic time series into permanent and transitory components with particular attention to measurement of the `business cycle'," Journal of Monetary Economics, Elsevier, vol. 7(2), pages 151-174.
    6. Baillie, Richard T. & Bollerslev, Tim & Mikkelsen, Hans Ole, 1996. "Fractionally integrated generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 74(1), pages 3-30, September.
    7. Bougerol, Philippe & Picard, Nico, 1992. "Stationarity of Garch processes and of some nonnegative time series," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 115-127.
    8. Davidson, James, 2004. "Moment and Memory Properties of Linear Conditional Heteroscedasticity Models, and a New Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 22(1), pages 16-29, January.
    9. Nelson, Daniel B., 1990. "Stationarity and Persistence in the GARCH(1,1) Model," Econometric Theory, Cambridge University Press, vol. 6(3), pages 318-334, September.
    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. Hualing Lin & Qiubi Sun & Sheng-Qun Chen, 2020. "Reducing Exchange Rate Risks in International Trade: A Hybrid Forecasting Approach of CEEMDAN and Multilayer LSTM," Sustainability, MDPI, vol. 12(6), pages 1-19, March.

    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. Li, Muyi & Li, Wai Keung & Li, Guodong, 2015. "A new hyperbolic GARCH model," Journal of Econometrics, Elsevier, vol. 189(2), pages 428-436.
    2. Charles, Amélie & Darné, Olivier, 2014. "Volatility persistence in crude oil markets," Energy Policy, Elsevier, vol. 65(C), pages 729-742.
    3. Pagan, Adrian, 1996. "The econometrics of financial markets," Journal of Empirical Finance, Elsevier, vol. 3(1), pages 15-102, May.
    4. Lahiani, Amine & Yousfi, Ouidad, 2007. "Modèls Garch à la mémoire longue: application aux taux de change tunisiens [GARCH models : evidence from Tunisian Exchange market]," MPRA Paper 28702, University Library of Munich, Germany, revised 2008.
    5. Eric Beutner & Alexander Heinemann & Stephan Smeekes, 2019. "A General Framework for Prediction in Time Series Models," Papers 1902.01622, arXiv.org.
    6. 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.
    7. Bollerslev, Tim & Ole Mikkelsen, Hans, 1996. "Modeling and pricing long memory in stock market volatility," Journal of Econometrics, Elsevier, vol. 73(1), pages 151-184, July.
    8. Christoffersen, Peter & Jacobs, Kris & Ornthanalai, Chayawat & Wang, Yintian, 2008. "Option valuation with long-run and short-run volatility components," Journal of Financial Economics, Elsevier, vol. 90(3), pages 272-297, December.
    9. Tim Bollerslev, 2008. "Glossary to ARCH (GARCH)," CREATES Research Papers 2008-49, Department of Economics and Business Economics, Aarhus University.
    10. HAFNER, Christian & PREMINGER, Arie, 2016. "On Asymptotic Theory for ARCH(infinite) Models," LIDAM Discussion Papers CORE 2016030, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    11. Lee, Oesook, 2018. "Stationarity and functional central limit theorem for ARCH(∞) models," Economics Letters, Elsevier, vol. 162(C), pages 107-111.
    12. Mawuli Segnon & Rangan Gupta & Keagile Lesame & Mark E. Wohar, 2021. "High-Frequency Volatility Forecasting of US Housing Markets," The Journal of Real Estate Finance and Economics, Springer, vol. 62(2), pages 283-317, February.
    13. Hidalgo, Javier & Zaffaroni, Paolo, 2007. "A goodness-of-fit test for ARCH([infinity]) models," Journal of Econometrics, Elsevier, vol. 141(2), pages 973-1013, December.
    14. Halkos, George & Tzirivis, Apostolos, 2018. "Effective energy commodities’ risk management: Econometric modeling of price volatility," MPRA Paper 90781, University Library of Munich, Germany.
    15. Harry Vander Elst, 2015. "FloGARCH : Realizing long memory and asymmetries in returns volatility," Working Paper Research 280, National Bank of Belgium.
    16. Conrad, Christian, 2010. "Non-negativity conditions for the hyperbolic GARCH model," Journal of Econometrics, Elsevier, vol. 157(2), pages 441-457, August.
    17. Christian Francq & Jean-Michel Zakoïan, 2013. "Optimal predictions of powers of conditionally heteroscedastic processes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(2), pages 345-367, March.
    18. Muyi Li & Wai Keung Li & Guodong Li, 2013. "On Mixture Memory Garch Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(6), pages 606-624, November.
    19. Nazim Regnard & Jean‐Michel Zakoïan, 2010. "Structure and estimation of a class of nonstationary yet nonexplosive GARCH models," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(5), pages 348-364, September.
    20. Han, Heejoon & Park, Joon Y., 2008. "Time series properties of ARCH processes with persistent covariates," Journal of Econometrics, Elsevier, vol. 146(2), pages 275-292, October.

    More about this item

    Keywords

    GARCH; FIGARCH; Conditional heteroscedasticity; Stationarity; Persistence; Forecasting;
    All these keywords.

    JEL classification:

    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

    Statistics

    Access and download statistics

    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:eee:empfin:v:38:y:2016:i:pb:p:534-547. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jempfin .

    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.