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Multimodality in the GARCH Regression Model

Author Info

  • 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.

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File URL: http://www.nuff.ox.ac.uk/economics/papers/2003/W20/GarchMode1.pdf
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Paper provided by Economics Group, Nuffield College, University of Oxford in its series Economics Papers with number 2003-W20.

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Length: 30 pages
Date of creation: 15 Sep 2003
Date of revision:
Handle: RePEc:nuf:econwp:0320
Contact details of provider: Web page: https://www.nuffield.ox.ac.uk/economics/

Keywords: Dummy variable; EGARCH; GARCH; Multimodality.;

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Find related papers by 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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  1. 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..
  2. Jurgen A. Doornik & Marius Ooms, 2005. "Outlier Detection in GARCH Models," Economics Papers 2005-W24, Economics Group, Nuffield College, University of Oxford.
  3. 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 229-35, April.
  4. 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.
  5. Drost, F.C. & Nijman, T.E., 1990. "Temporal Aggregation Of Garch Processes," Papers 9066, Tilburg - Center for Economic Research.
  6. Neil Shephard, 2005. "Stochastic Volatility," Economics Papers 2005-W17, Economics Group, Nuffield College, University of Oxford.
  7. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
  8. Drost, F.C. & Nijman, T.E., 1993. "Temporal aggregation of GARCH processes," Other publications TiSEM 0642fb61-c7f4-4281-b484-4, Tilburg University, School of Economics and Management.
  9. 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.
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Cited by:

  1. Jurgen Doornik & Marius Ooms, 2005. "Outlier Detection in GARCH Models," Economics Series Working Papers 2005-W24, University of Oxford, Department of Economics.
  2. 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.
  3. Hillebrand, Eric & Schnabl, Gunther, 2006. "A structural break in the effects of Japanese foreign exchange intervention on yen/dollar exchange rate volatility," Working Paper Series 0650, European Central Bank.
  4. Bernd Hayo & Ali M. Kutan, 2004. "The Impact of News, Oil Prices, and Global Market Developments on Russian Financial Markets," William Davidson Institute Working Papers Series 2004-656, William Davidson Institute at the University of Michigan.
  5. Coffinet, J. & Frappa, S., 2008. "Macroeconomic Surprises and the Inflation Compensation Curve in the Euro Area," Working papers 220, Banque de France.
  6. Carmen Broto, 2012. "The effectiveness of forex interventions in four Latin American countries," Working Papers 1226, Banco de España;Working Papers Homepage.
  7. Manfred Gilli & Peter Winker, 2008. "Review of Heuristic Optimization Methods in Econometrics," Working Papers 001, COMISEF.
  8. 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, EconWPA.
  9. Bernd Hayo & Ali Kutan, 2002. "The Impact of News, Oil Prices, and International Spillovers on Russian Financial Markets," Finance 0209001, EconWPA.
  10. Mark, Joy, 2011. "Gold and the US dollar: Hedge or haven?," Finance Research Letters, Elsevier, vol. 8(3), pages 120-131, September.
  11. 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.
  12. 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.

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