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Multimodality in the GARCH Regression Model

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  • Jurgen Doornik
  • Marius Ooms

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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Bibliographic Info

Paper provided by University of Oxford, Department of Economics in its series Economics Series Working Papers with number 2003-W20.

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Date of creation: 01 Oct 2003
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Handle: RePEc:oxf:wpaper:2003-w20

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Keywords: dummy variable; EGARCH; GARCH; multimodality;

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  1. Drost, F.C. & Nijman, T.E., 1990. "Temporal aggregation of GARCH processes," Discussion Paper 1990-66, Tilburg University, Center for Economic Research.
  2. Jurgen A. Doornik & Marius Ooms, 2005. "Outlier Detection in GARCH Models," Tinbergen Institute Discussion Papers 05-092/4, Tinbergen Institute.
  3. 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.
  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. Neil Shephard, 2005. "Stochastic Volatility," Economics Papers 2005-W17, Economics Group, Nuffield College, University of Oxford.
  6. 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.
  7. 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.
  8. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
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Citations

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Cited by:
  1. Coffinet, J. & Frappa, S., 2008. "Macroeconomic Surprises and the Inflation Compensation Curve in the Euro Area," Working papers 220, Banque de France.
  2. Hayo, Bernd & Kutan, Ali M., 2002. "The impact of news, oil prices, and international spillovers on Russian financial markets," ZEI Working Papers B 20-2002, ZEI - Center for European Integration Studies, University of Bonn.
  3. 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.
  4. 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.
  5. Jurgen A. Doornik & Marius Ooms, 2005. "Outlier Detection in GARCH Models," Tinbergen Institute Discussion Papers 05-092/4, Tinbergen Institute.
  6. Carmen Broto, 2012. "The effectiveness of forex interventions in four Latin American countries," Banco de Espa�a Working Papers 1226, Banco de Espa�a.
  7. 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.
  8. Bernd Hayo & Ali Kutan, 2004. "The Impact of News, Oil Prices, and Global Market Developments on Russian Financial Markets," Finance 0403002, EconWPA.
  9. Mark, Joy, 2011. "Gold and the US dollar: Hedge or haven?," Finance Research Letters, Elsevier, vol. 8(3), pages 120-131, September.
  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, EconWPA.
  11. Manfred Gilli & Peter Winker, 2008. "Review of Heuristic Optimization Methods in Econometrics," Working Papers 001, COMISEF.
  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.

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