10.2 Some Multivariate GARCH Models
Many authors have generalized univariate volatility models to the multivariate case. In this section, we discuss some of the generalizations. For more details, readers are referred to the survey article of Bauwens, Laurent, and Rombouts (2004).
10.2.1 Diagonal Vectorization (VEC) Model
Bollerslev, Engle, and Wooldridge (1988) generalize the exponentially weighted moving-average approach to propose the model
10.5 
where m and s are nonnegative integers, 
and 
are symmetric matrices, and ⊙ denotes the Hadamard product, that is, element-by-element multiplication. This is referred to as the diagonal VEC(m, s) model or DVEC(m, s) model. To appreciate the model, consider the bivariate DVEC(1,1) case satisfying
where only the lower triangular part of the model is given. Specifically, the model is
where each element of 
depends only on its own past value and the ...
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