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2019 On limit theory for functionals of stationary increments Lévy driven moving averages
Andreas Basse-O’Connor, Claudio Heinrich, Mark Podolskij
Electron. J. Probab. 24: 1-42 (2019). DOI: 10.1214/19-EJP336

Abstract

In this paper we present new limit theorems for variational functionals of stationary increments Lévy driven moving averages in the high frequency setting. More specifically, we will show the “law of large numbers” and a “central limit theorem”, which heavily rely on the kernel, the driving Lévy process and the properties of the functional under consideration. The first order limit theory consists of three different cases. For one of the appearing limits, which we refer to as the ergodic type limit, we prove the associated weak limit theory, which again consists of three different cases. Our work is related to [10, 7], who considered power variation functionals of stationary increments Lévy driven moving averages. However, the asymptotic theory of the present paper is more complex. In particular, the weak limit theorems are derived for an arbitrary Appell rank of the involved functional.

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Andreas Basse-O’Connor. Claudio Heinrich. Mark Podolskij. "On limit theory for functionals of stationary increments Lévy driven moving averages." Electron. J. Probab. 24 1 - 42, 2019. https://doi.org/10.1214/19-EJP336

Information

Received: 23 July 2018; Accepted: 18 June 2019; Published: 2019
First available in Project Euclid: 5 September 2019

zbMATH: 07107386
MathSciNet: MR4003132
Digital Object Identifier: 10.1214/19-EJP336

Subjects:
Primary: 60F05, 60F17, 60G22, 60G52

JOURNAL ARTICLE
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