IDEAS home Printed from https://ideas.repec.org/p/nuf/econwp/0320.html
   My bibliography  Save this paper

Multimodality in the GARCH Regression Model

Author

Listed:
  • Jurgen A. Doornik

    (Nuffield College, University of Oxford)

  • Marius Ooms

    (Dept of Econometrics, Free University Amsterdam)

Abstract

Several aspects of GARCH(p,q) models that are relevant for empirical applications are investigated. In particular, it is noted that the inclusion of dummy variables as regressors can lead to multimodality in the GARCH likelihood. This invalidates standard inference on the estimated coefficients. Next, the implementation of different restrictions on the GARCH parameter space is considered. A refinement to the Nelson and Cao (1992) conditions for a GARCH(2,q) model is presented, and it is shown how these can then be implemented by parameter transformations. It is argued that these conditions may also be too restrictive, and a simpler alternative is introduced which is formulated in terms of the unconditional variance. Finally, examples show that multimodality is a real concern for models of the £/$ exchange rate, especially when p>2.

Suggested Citation

  • Jurgen A. Doornik & Marius Ooms, 2003. "Multimodality in the GARCH Regression Model," Economics Papers 2003-W20, Economics Group, Nuffield College, University of Oxford.
    • Handle: RePEc:nuf:econwp:0320
    as

    Download full text from publisher

    File URL: http://www.nuff.ox.ac.uk/economics/papers/2003/W20/GarchMode1.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Drost, Feike C & Nijman, Theo E, 1993. "Temporal Aggregation of GARCH Processes," Econometrica, Econometric Society, vol. 61(4), pages 909-927, July.
    2. Bollerslev, Tim & Engle, Robert F. & Nelson, Daniel B., 1986. "Arch models," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 49, pages 2959-3038, Elsevier.
    3. Changli He & Timo Terasvirta, 1999. "Properties of the Autocorrelation Function of Squared Observations for Second‐order Garch Processes Under Two Sets of Parameter Constraints," Journal of Time Series Analysis, Wiley Blackwell, vol. 20(1), pages 23-30, January.
    4. van Dijk, Dick & Franses, Philip Hans & Lucas, Andre, 1999. "Testing for ARCH in the Presence of Additive Outliers," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 14(5), pages 539-562, Sept.-Oct.
    5. M. Angeles Carnero & Daniel Peña & Esther Ruiz, 2007. "Effects of outliers on the identification and estimation of GARCH models," Journal of Time Series Analysis, Wiley Blackwell, vol. 28(4), pages 471-497, July.
    6. Jurgen A. Doornik & Marius Ooms, 2005. "Outlier Detection in GARCH Models," Tinbergen Institute Discussion Papers 05-092/4, Tinbergen Institute.
    7. Doornik Jurgen A & Ooms Marius, 2004. "Inference and Forecasting for ARFIMA Models With an Application to US and UK Inflation," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 8(2), pages 1-25, May.
    8. Fiorentini, Gabriele & Calzolari, Giorgio & Panattoni, Lorenzo, 1996. "Analytic Derivatives and the Computation of GARCH Estimates," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 11(4), pages 399-417, July-Aug..
    9. Franses, Philip Hans & Ghijsels, Hendrik, 1999. "Additive outliers, GARCH and forecasting volatility," International Journal of Forecasting, Elsevier, vol. 15(1), pages 1-9, February.
    10. Ledolter, Johannes, 1989. "The effect of additive outliers on the forecasts from ARIMA models," International Journal of Forecasting, Elsevier, vol. 5(2), pages 231-240.
    11. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    12. Geweke, John, 2007. "Interpretation and inference in mixture models: Simple MCMC works," Computational Statistics & Data Analysis, Elsevier, vol. 51(7), pages 3529-3550, April.
    13. Neil Shephard, 2005. "Stochastic Volatility," Economics Papers 2005-W17, Economics Group, Nuffield College, University of Oxford.
    14. Nelson, Daniel B & Cao, Charles Q, 1992. "Inequality Constraints in the Univariate GARCH Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(2), pages 229-235, April.
    15. Baillie, Richard T & Chung, Ching-Fan & Tieslau, Margie A, 1996. "Analysing Inflation by the Fractionally Integrated ARFIMA-GARCH Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 11(1), pages 23-40, Jan.-Feb..
    16. Gomez, Victor & Maravall, Agustin & Pena, Daniel, 1998. "Missing observations in ARIMA models: Skipping approach versus additive outlier approach," Journal of Econometrics, Elsevier, vol. 88(2), pages 341-363, November.
    17. Nelson, Daniel B & Foster, Dean P, 1994. "Asymptotic Filtering Theory for Univariate ARCH Models," Econometrica, Econometric Society, vol. 62(1), pages 1-41, January.
    18. 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)

    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. Charles, Amélie & Darné, Olivier, 2014. "Volatility persistence in crude oil markets," Energy Policy, Elsevier, vol. 65(C), pages 729-742.
    2. Grané, Aurea & Veiga, Helena, 2010. "Outliers in Garch models and the estimation of risk measures," DES - Working Papers. Statistics and Econometrics. WS ws100502, Universidad Carlos III de Madrid. Departamento de Estadística.
    3. Jurgen A. Doornik & Marius Ooms, 2000. "Multimodality and the GARCH Likelihood," Econometric Society World Congress 2000 Contributed Papers 0798, Econometric Society.
    4. Veiga, Helena, 2009. "Wavelet-based detection of outliers in volatility models," DES - Working Papers. Statistics and Econometrics. WS ws090403, Universidad Carlos III de Madrid. Departamento de Estadística.
    5. Charles, Amélie & Darné, Olivier, 2014. "Large shocks in the volatility of the Dow Jones Industrial Average index: 1928–2013," Journal of Banking & Finance, Elsevier, vol. 43(C), pages 188-199.
    6. Grané, Aurea & Veiga, Helena, 2010. "Wavelet-based detection of outliers in financial time series," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2580-2593, November.
    7. Lisa Crosato & Luigi Grossi, 2019. "Correcting outliers in GARCH models: a weighted forward approach," Statistical Papers, Springer, vol. 60(6), pages 1939-1970, December.
    8. Behmiri, Niaz Bashiri & Manera, Matteo, 2015. "The role of outliers and oil price shocks on volatility of metal prices," Resources Policy, Elsevier, vol. 46(P2), pages 139-150.
    9. David McMillan & Alan Speight, 2006. "Heterogeneous information flows and intra-day volatility dynamics: evidence from the UK FTSE-100 stock index futures market," Applied Financial Economics, Taylor & Francis Journals, vol. 16(13), pages 959-972.
    10. Tim Bollerslev, 2008. "Glossary to ARCH (GARCH)," CREATES Research Papers 2008-49, Department of Economics and Business Economics, Aarhus University.
    11. Amélie Charles, 2008. "Forecasting volatility with outliers in GARCH models," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 27(7), pages 551-565.
    12. E. Ruiz & M.A. Carnero & D. Pereira, 2004. "Effects of Level Outliers on the Identification and Estimation of GARCH Models," Econometric Society 2004 Australasian Meetings 21, Econometric Society.
    13. Carnero, María Ángeles, 2001. "Outliers and conditional autoregressive heteroscedasticity in time series," DES - Working Papers. Statistics and Econometrics. WS ws010704, Universidad Carlos III de Madrid. Departamento de Estadística.
    14. 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.
    15. Torben G. Andersen & Tim Bollerslev, 1997. "Answering the Critics: Yes, ARCH Models Do Provide Good Volatility Forecasts," NBER Working Papers 6023, National Bureau of Economic Research, Inc.
    16. 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.
    17. Sébastien Laurent & Luc Bauwens & Jeroen V. K. Rombouts, 2006. "Multivariate GARCH models: a survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(1), pages 79-109.
    18. Drost, Feike C. & Werker, Bas J. M., 1996. "Closing the GARCH gap: Continuous time GARCH modeling," Journal of Econometrics, Elsevier, vol. 74(1), pages 31-57, September.
    19. Meddahi, Nour & Renault, Eric, 2004. "Temporal aggregation of volatility models," Journal of Econometrics, Elsevier, vol. 119(2), pages 355-379, April.
    20. Font, Begoña, 1998. "Modelización de series temporales financieras. Una recopilación," DES - Documentos de Trabajo. Estadística y Econometría. DS 3664, Universidad Carlos III de Madrid. Departamento de Estadística.

    More about this item

    Keywords

    Dummy variable; EGARCH; GARCH; Multimodality.;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:nuf:econwp:0320. 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: Maxine Collett (email available below). General contact details of provider: https://www.nuffield.ox.ac.uk/economics/ .

    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.