Multimodality and the GARCH Likelihood
AbstractWe investigate several aspects of GARCH(p,q) 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-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 pounds exchange rate, and should be taken account of, especially when p >= 2.
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Bibliographic InfoPaper provided by Society for Computational Economics in its series Computing in Economics and Finance 2001 with number 76.
Date of creation: 01 Apr 2001
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GARCH; EGARCH; multimodality; dummy variable; parameter space;
Other versions of this item:
- Jurgen A. Doornik & Marius Ooms, 2000. "Multimodality and the GARCH Likelihood," Econometric Society World Congress 2000 Contributed Papers 0798, Econometric Society.
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models &bull Diffusion Processes
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