Template-type: ReDIF-Paper 1.0
Author-Name:Jurgen A. Doornik
Author-Email:jurgen.doornik@nuffield.ox.ac.uk
Author-Workplace-Name:Nuffield College, University of Oxford
Author-Name:Marius Ooms
Author-Workplace-Name:Dept of Econometrics, Free University Amsterdam
Title: Multimodality in the GARCH Regression Model
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.
Classification-JEL:C22, C51
Keywords:Dummy variable, EGARCH, GARCH, Multimodality.
Length:30 pages
Creation-Date: 2003-09-15
Number:2003-W20
File-URL: http://www.nuff.ox.ac.uk/economics/papers/2003/W20/GarchMode1.pdf
File-Format: application/pdf
Handle: RePEc:nuf:econwp:0320