鞅的已实现累积量

arXiv: Probability Pub Date : 2020-10-16 DOI:10.1214/21-ECP382

M. Fukasawa, Kazuki Matsushita

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引用次数: 5

摘要

将已实现的方差、已实现的偏度(Neuberger, 2012)和已实现的峰度(Bae和Lee, 2020)一般化，我们构建具有所谓聚集特性的已实现累积量。它们是基于鞅及其低阶条件累积过程的子周期增量的鞅边际累积量的无偏统计量。我们的关键发现是聚集性质与完全贝尔多项式之间的关系。

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Realized cumulants for martingales

Generalizing the realized variance, the realized skewness (Neuberger, 2012) and the realized kurtosis (Bae and Lee, 2020), we construct realized cumulants with the so-called aggregation property. They are unbiased statistics of the cumulants of a martingale marginal based on sub-period increments of the martingale and its lower-order conditional cumulant processes. Our key finding is a relation between the aggregation property and the complete Bell polynomials.

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arXiv: Probability

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