ON THE RELATION BETWEEN THE VEC AND BEKK MULTIVARIATE GARCH MODELS
研究了哪些VEC形式的多元GARCH模型可以表示为BEKK形式，利用线性代数结果证明所有不能表示为最简单BEKK形式的VEC模型都包含将向量化半正定矩阵映射到其严格子集的参数矩阵，并给出二维等价、三维存在反例的结论。
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.