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Multimodality in GARCH regression models

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  • Doornik, Jurgen A.
  • Ooms, Marius

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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Suggested Citation

  • Doornik, Jurgen A. & Ooms, Marius, 2008. "Multimodality in GARCH regression models," International Journal of Forecasting, Elsevier, vol. 24(3), pages 432-448.
  • Handle: RePEc:eee:intfor:v:24:y:2008:i:3:p:432-448
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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. 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.
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    More about this item

    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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