论文标题
多元连续时间自回归运动平均流程在锥体上
Multivariate continuous-time autoregressive moving-average processes on cones
论文作者
论文摘要
在本文中，我们研究了具有凸锥值的多元连续时间自回归运动平均（MCARMA）过程。更具体地说，我们引入了具有Lévy噪声的基质值MCARMA工艺，并提供了从该类别的过程中的必要和足够条件。在以下两种情况下，我们在$ \ mathbb {r} _ {d} $上获得了特定的动手条件：首先，在正晶体$ \ mathbb {r} _ {r} _ {d} _ {d}^{+} $中，带有值。其次，对于MCARMA过程，在对称和阳性半明确矩阵的锥体中采用值的MCARMA过程。两种情况都与应用有关，我们提供了几个阳性示例，以确保参数规格。除上述内容外，我们还讨论了半半决赛MCARMA过程的能力，以模拟多元随机波动率模型中的点协方差过程。我们通过对基于半决赛正平衡的Ornstein-uhlenbeck模型的二阶结构进行示例性分析来证明基于MCARMA的随机波动率模型的相关性。
In this article we study multivariate continuous-time autoregressive moving-average (MCARMA) processes with values in convex cones. More specifically, we introduce matrix-valued MCARMA processes with Lévy noise and present necessary and sufficient conditions for processes from this class to be cone valued. We derive specific hands-on conditions in the following two cases: First, for classical MCARMA on $\mathbb{R}_{d}$ with values in the positive orthant $\mathbb{R}_{d}^{+}$. Second, for MCARMA processes on real square matrices taking values in the cone of symmetric and positive semi-definite matrices. Both cases are relevant for applications and we give several examples of positivity ensuring parameter specifications. In addition to the above, we discuss the capability of positive semi-definite MCARMA processes to model the spot covariance process in multivariate stochastic volatility models. We justify the relevance of MCARMA based stochastic volatility models by an exemplary analysis of the second order structure of positive semi-definite well-balanced Ornstein-Uhlenbeck based models.
