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2021 Realized cumulants for martingales
Masaaki Fukasawa, Kazuki Matsushita
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Electron. Commun. Probab. 26: 1-10 (2021). DOI: 10.1214/21-ECP382

Abstract

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).

Citation

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Masaaki Fukasawa. Kazuki Matsushita. "Realized cumulants for martingales." Electron. Commun. Probab. 26 1 - 10, 2021. https://doi.org/10.1214/21-ECP382

Information

Received: 16 October 2020; Accepted: 17 February 2021; Published: 2021
First available in Project Euclid: 23 March 2021

Digital Object Identifier: 10.1214/21-ECP382

Subjects:
Primary: 60G44

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