The multivariate skewed variance gamma (MSVG) distribution is useful in modelling data with high density around the location parameter along with moderate heavy-tailedness. However, the density can be unbounded for certain choices of shape parameter. We propose a modification to the expectation-conditional maximisation (ECM) algorithm to calculate the maximum likelihood estimate (MLE) by introducing a small region to cap the conditional expectations in order to deal with the unbounded density. To facilitate application to financial time series, the mean is further extended to include autoregressive terms. Finally, the MSVG model is applied to analyse the returns of five daily closing price market indices. Standard error (SE) for the estimated parameters are computed using Louis’ method.

中文翻译：

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具有无界密度的自回归多元斜方差伽马模型的ECM算法

多元偏斜方差伽玛（MSVG）分布可用于对位置参数周围的高密度数据和适度的重尾数据进行建模。但是，对于某些形状参数选择，密度可以不受限制。我们提出了对期望条件最大化（ECM）算法的一种修改，以通过引入一个较小的区域来覆盖条件期望值以计算无限密度来计算最大似然估计（MLE）。为便于应用于金融时间序列，均值进一步扩展为包括自回归项。最后，使用MSVG模型分析五个每日收盘价市场指数的回报。使用路易斯方法计算估计参数的标准误差（SE）。