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Multimodality and the GARCH Likelihood

Author

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  • Jurgen A. Doornik

    (Nuffield College)

  • Marius Ooms

    (Free University Amsterdam)

Abstract

We investigate several aspects of GARCH models which are relevant for empirical applications. In particular, we note that the inclusion of a dummy variable as regressor can lead to multimodality in the GARCH likelihood. This makes standard inference on the estimated coefficient impossible. Next, we investigate the implementation of different restrictions on the GARCH parameter space. We present a small refinement to the Nelson and Cao (1992) conditions for a GARCH(2,q) model, and show how these can be implemented by parameter transformations. We argue that these conditions are also too restrictive, and consider restrictions which are formulated in terms of the unconditional variance. These are easier to work with and understand. Finally, we show that multimodality is a real concern for models of the pound/dollar exchange rate, and should be taken account of, especially when p>=2.

Suggested Citation

  • Jurgen A. Doornik & Marius Ooms, 2000. "Multimodality and the GARCH Likelihood," Econometric Society World Congress 2000 Contributed Papers 0798, Econometric Society.
  • Handle: RePEc:ecm:wc2000:0798
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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.
    2. Drost, Feike C & Nijman, Theo E, 1993. "Temporal Aggregation of GARCH Processes," Econometrica, Econometric Society, vol. 61(4), pages 909-927, July.
    3. Neil Shephard, 2005. "Stochastic Volatility," Economics Papers 2005-W17, Economics Group, Nuffield College, University of Oxford.
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    6. Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 2002. "Bayesian Analysis of Stochastic Volatility Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 69-87, January.
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    8. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
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    Cited by:

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    2. Eric Hillebrand & Gunther Schnabl, 2003. "The Effects of Japanese Foreign Exchange Intervention: GARCH Estimation and Change Point Detection," Departmental Working Papers 2003-09, Department of Economics, Louisiana State University.
    3. Kwami Adanu, 2006. "Optimizing the Garch Model–An Application of Two Global and Two Local Search Methods," Computational Economics, Springer;Society for Computational Economics, vol. 28(3), pages 277-290, October.
    4. Soosung Hwang & Pedro L. Valls Pereira, 2006. "Small sample properties of GARCH estimates and persistence," The European Journal of Finance, Taylor & Francis Journals, vol. 12(6-7), pages 473-494.
    5. Laurini, Márcio Poletti & Portugal, Marcelo Savino, 2004. "Long memory in the R$ / US$ exchange rate: A robust analysis," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 24(1), May.
    6. Hillebrand, Eric, 2005. "Neglecting parameter changes in GARCH models," Journal of Econometrics, Elsevier, vol. 129(1-2), pages 121-138.
    7. Henrik Amilon, 2002. "A Score Test for Discreteness in GARCH Models," Research Paper Series 76, Quantitative Finance Research Centre, University of Technology, Sydney.
    8. Amilon, Henrik, 2003. "GARCH estimation and discrete stock prices: an application to low-priced Australian stocks," Economics Letters, Elsevier, vol. 81(2), pages 215-222, November.
    9. Yi-Chi Chen, 2013. "The Dynamics of Interbank Rate Behavior Under Alternative Monetary Regimes: The Case of Hong Kong," China Economic Policy Review (CEPR), World Scientific Publishing Co. Pte. Ltd., vol. 2(02), pages 1-21.

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    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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