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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
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    File URL: http://www.nuff.ox.ac.uk/economics/papers/2003/W20/GarchMode1.pdf
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    References listed on IDEAS

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    1. Drost, Feike C & Nijman, Theo E, 1993. "Temporal Aggregation of GARCH Processes," Econometrica, Econometric Society, vol. 61(4), pages 909-927, July.
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    3. Jurgen A. Doornik & Marius Ooms, 2005. "Outlier Detection in GARCH Models," Tinbergen Institute Discussion Papers 05-092/4, Tinbergen Institute.
    4. 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..
    5. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    6. Neil Shephard, 2005. "Stochastic Volatility," Economics Papers 2005-W17, Economics Group, Nuffield College, University of Oxford.
    7. 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.
    8. 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.
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    Citations

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    Cited by:

    1. Baoying Lai & Nathan Lael Joseph, 2010. "Pricing-to-market and the volatility of UK export prices," Applied Financial Economics, Taylor & Francis Journals, vol. 20(18), pages 1441-1460.
    2. Kim, Suk-Joong, 2007. "Intraday evidence of efficacy of 1991-2004 Yen intervention by the Bank of Japan," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 17(4), pages 341-360, October.
    3. Eric Hillebrand & Gunther Schnabl, 2008. "A structural break in the effects of Japanese foreign exchange intervention on yen/dollar exchange rate volatility," International Economics and Economic Policy, Springer, vol. 5(4), pages 389-401, December.
    4. Jurgen A. Doornik & Marius Ooms, 2005. "Outlier Detection in GARCH Models," Tinbergen Institute Discussion Papers 05-092/4, Tinbergen Institute.
    5. Coffinet, J. & Frappa, S., 2008. "Macroeconomic Surprises and the Inflation Compensation Curve in the Euro Area," Working papers 220, Banque de France.
    6. Bernd Hayo & Ali Kutan, 2002. "The Impact of News, Oil Prices, and International Spillovers on Russian Financial Markets," Finance 0209001, University Library of Munich, Germany.
    7. Bernd Hayo & Ali M. Kutan, 2005. "The impact of news, oil prices, and global market developments on Russian financial markets," The Economics of Transition, The European Bank for Reconstruction and Development, vol. 13(2), pages 373-393, April.
    8. Manfred GILLI & Peter WINKER, "undated". "A review of heuristic optimization methods in econometrics," Swiss Finance Institute Research Paper Series 08-12, Swiss Finance Institute.
    9. Broto, Carmen, 2013. "The effectiveness of forex interventions in four Latin American countries," Emerging Markets Review, Elsevier, vol. 17(C), pages 224-240.
    10. Maurício Yoshinori Une & Marcelo Savino Portugal, 2005. "Can fear beat hope? A story of GARCH-in-Mean-Level effects for Emerging Market Country Risks," Econometrics 0509006, University Library of Munich, Germany.
    11. Mark, Joy, 2011. "Gold and the US dollar: Hedge or haven?," Finance Research Letters, Elsevier, vol. 8(3), pages 120-131, September.
    12. Pascual, Lorenzo & Romo, Juan & Ruiz, Esther, 2006. "Bootstrap prediction for returns and volatilities in GARCH models," Computational Statistics & Data Analysis, Elsevier, vol. 50(9), pages 2293-2312, May.

    More about this item

    Keywords

    Dummy variable; EGARCH; GARCH; Multimodality.;

    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

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