Nuisance parameters, composite likelihoods and a panel of GARCH models

We investigate the properties of the composite likelihood (CL) method for (T x NT) GARCH panels.  The defining feature of a GARCH panel with time series length T is that, while nuisance parameters are allowed to vary across NT series, other parameters of interest are assumed to be common.  CL pools information across the panel instead of using information available in a single series only.  Simulations and empirical analysis illustate that in reasonably large T CL performs well.  However, due to the estimation error introduced through nuisance parameter estimation, CL is subject to the "incidental parameter" problem for small T.