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Analysis of Financial Time Series, Third Edition by RUEY S. TSAY

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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 10.5

where m and s are nonnegative integers, inline and inline 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

inline

where only the lower triangular part of the model is given. Specifically, the model is

inline

where each element of inline depends only on its own past value and the ...

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