Multimodality and the GARCH Likelihood

Jurgen Doornik and Marius Ooms

No 798, Econometric Society World Congress 2000 Contributed Papers from Econometric Society

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.

Date: 2000-08-01
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Citations: View citations in EconPapers (10)

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Working Paper: Multimodality and the GARCH Likelihood (2001)
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