文章基本信息

标题：Realized cumulants for martingales
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作者：Masaaki Fukasawa ; Kazuki Matsushita
期刊名称：Electronic Communications in Probability
印刷版ISSN：1083-589X
出版年度：2021
卷号：26
页码：1-10
DOI：10.1214/21-ECP382
语种：English
出版社：Electronic Communications in Probability
摘要：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. For an application we give an alternative proof and an extension of a cumulant recursion formula recently obtained by Lacoin et al. (2019) and Friz et al. (2020).
关键词：60G44; aggregation property; cumulant; high-frequency data; martingale