Multimodality in GARCH regression models

M. Ooms, J.A. Doornik

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It is shown empirically that mixed autoregressive moving average regression models with generalized autoregressive conditional heteroskedasticity (Reg-ARMA-GARCH models) can have multimodality in the likelihood that is caused by a dummy variable in the conditional mean. Maximum likelihood estimates at the local and global modes are investigated and turn out to be qualitatively different, leading to different model-based forecast intervals. In the simpler GARCH(p,q) regression model, we derive analytical conditions for bimodality of the corresponding likelihood. In that case, the likelihood is symmetrical around a local minimum. We propose a solution to avoid this bimodality. © 2008 International Institute of Forecasters.
Original languageUndefined/Unknown
Pages (from-to)432-448
JournalInternational Journal of Forecasting
Issue number3
Publication statusPublished - 2008

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