论文标题
多变量尾部充气的正态分布及其在金融中的应用
The multivariate tail-inflated normal distribution and its application in finance
论文作者
论文摘要
本文介绍了多元尾液的正常（MTIN）分布，这是多元正常（MN）的椭圆形重尾概括。 MTIN通过选择方便的连续均匀作为混合分布而属于MN量表混合物的家族。此外，对于嵌套的MN而言，它的概率密度函数具有封闭形式，其特征在于嵌套的MN，控制尾部重量。还计算了前四个时刻；有趣的是，它们始终存在，多余的峰度可以假设任何正值。考虑估计的矩和最大似然方法（ML）。如后者所关注的那样，说明了一种直接方法以及EM算法的变体。还评估了ML估计值的存在。由于从数据估算了通货膨胀参数，因此嵌套MN分布的平均向量和协方差矩阵的鲁棒估计是通过下降加权自动获得的。进行仿真以比较估计方法/算法，并研究AIC和BIC在一组候选椭圆模型中选择的能力。出于说明目的，MTIN分布最终适用于多元财务数据，在该数据中，与其他良好的多元椭圆分布相比，其有用性也显示出来。
This paper introduces the multivariate tail-inflated normal (MTIN) distribution, an elliptical heavy-tails generalization of the multivariate normal (MN). The MTIN belongs to the family of MN scale mixtures by choosing a convenient continuous uniform as mixing distribution. Moreover, it has a closed-form for the probability density function characterized by only one additional ``inflation'' parameter, with respect to the nested MN, governing the tail-weight. The first four moments are also computed; interestingly, they always exist and the excess kurtosis can assume any positive value. The method of moments and maximum likelihood (ML) are considered for estimation. As concerns the latter, a direct approach, as well as a variant of the EM algorithm, are illustrated. The existence of the ML estimates is also evaluated. Since the inflation parameter is estimated from the data, robust estimates of the mean vector and covariance matrix of the nested MN distribution are automatically obtained by down-weighting. Simulations are performed to compare the estimation methods/algorithms and to investigate the ability of AIC and BIC to select among a set of candidate elliptical models. For illustrative purposes, the MTIN distribution is finally fitted to multivariate financial data where its usefulness is also shown in comparison with other well-established multivariate elliptical distributions.
