Multimodality in GARCH regression models

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 conditinal mean. Maximum likelihood estimates at the local and global models 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 conditins for bimodality of the corresponding likelihood. In that case, the likelihood is symmertical around a local minimum. We propose a solution to avoid this bimodality. (C) International Institute of Forecasters. Published by Elsevier B.V. All rights reserved.