Probability distributions for realized covariance measures
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已实现协方差度量的概率分布
- 研究问题
- 如何为已实现协方差矩阵选择合理的概率分布，使其能够描述危机期间矩阵元素的尾部依赖，并用于建模和预测？
- 方法与思路
- 作者用随机上下三角矩阵的随机表示统一推导既有分布，提出具有尾部同质性的 t-Riesz 分布族并开展实证比较。
- 材料陈述的贡献
- 摘要称新分布族可刻画大协方差状态下元素间的高依赖，揭示各分布的理论联系，并在所考察样本中取得最佳拟合。
- 阅读关注点
- 应核对尾部同质性的数学定义、分布参数与矩存在条件，以及拟合和样本外预测比较采用的损失函数及基准。
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- 仅据所给 OpenAlex 摘要，不能确认优势适用于其他市场或风险任务；摘要未说明样本、预测期限和比较结果的数值。
原文摘要
Realized covariance measures (RCs) are an essential input for assessing the risks of different investment allocations. Thus, it is useful to model and forecast them. To this end, a realistic distributional assumption is needed. In this paper, we compare all probability distributions that have so far in the literature been applied to time-series of RCs. We derive them in a unified framework based on their stochastic representations using random lower and upper triangular matrices. These matrices are composed of standard normal distributions in the off-diagonal elements and χ -distributions on the diagonals (Barlett matrices). Furthermore, we derive a novel family of probability distributions (the t -Riesz distribution family), which has a property we call tail-homogeneity . This property means that in crisis periods, i.e. large RCs, our distribution family realistically assumes high dependence between the individual entries of the RCs. We show theoretically how all the distributions differ from each other, and how they are related to each other. In the empirical part, we demonstrate how the theoretical differences translate into differences in fit and forecasting performance. We show that our novel distribution family achieves the best fit. Out-of-sample forecasting comparisons further corroborate the excellent performance of our novel distribution family.