Interactions among multiple time series of positive random variables are crucial in diverse financial applications, from spillover effects to volatility interdependence. A popular model in this setting is the vector Multiplicative Error Model (vMEM) which poses a linear iterative structure on the dynamics of the conditional mean, perturbed by a multiplicative innovation term. A main limitation of vMEM is however its restrictive assumption on the distribution of the random innovation term. A Bayesian semiparametric approach that models the innovation vector as an infinite location-scale mixture of multidimensional kernels with support on the positive orthant is used to address this major shortcoming of vMEM. Computational complications arising from the constraints to the positive orthant are avoided through the formulation of a slice sampler on the parameter-extended unconstrained version of the model. The method is applied to simulated and real data and a flexible specification is obtained that outperforms the classical ones in terms of fitting and predictive power.

从溢出效应到波动性相互依存，正向随机变量的多个时间序列之间的相互作用对于多样化的金融应用至关重要。在这种情况下，流行的模型是向量乘性误差模型（vMEM），它在条件均值的动力学上构成线性迭代结构，并受到乘性创新项的干扰。然而，vMEM的主要局限性是其对随机创新项分布的限制性假设。一种贝叶斯半参数方法，用于将创新矢量建模为多维核的无限位置尺度混合并在正向正构体上提供支持，以解决vMEM的这一主要缺点。通过在模型的参数扩展的无约束版本上构造切片采样器，可以避免由于对正正齿约束的限制而导致的计算复杂性。该方法应用于模拟和真实数据，并且在拟合和预测能力方面获得了优于传统方法的灵活规范。