Abstract :
The question of which multivariate generalized autoregressive conditionally heteroskedastic
~GARCH! models in the vec form are representable in the BEKK
form is addressed+ Using results from linear algebra, it is established that all vec
models not representable in the simplest BEKK form contain matrices as parameters
that map the vectorized positive semidefinite matrices into a strict subset of
themselves+ Moreover, a general result from linear algebra is presented implying
that in dimension two the models are equivalent, and in dimension three a simple
analytically tractable example for a vec model having no BEKK representation is
given+
