On limit theory for functionals of stationary increments Lévy driven moving averages | Zendy

Andreas Basse-O’Connor | Zendy; Claudio Heinrich | Zendy; Mark Podolskij | Zendy

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On limit theory for functionals of stationary increments Lévy driven moving averages

Author(s) -

Andreas Basse-O’Connor,

Claudio Heinrich,

Mark Podolskij

Publication year - 2019

Publication title -

electronic journal of probability

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.666

H-Index - 53

ISSN - 1083-6489

DOI - 10.1214/19-ejp336

Subject(s) - mathematics , limit (mathematics) , ergodic theory , central limit theorem , rank (graph theory) , asymptotic analysis , stationary ergodic process , law of large numbers , kernel (algebra) , uniform limit theorem , lévy process , mathematical analysis , pure mathematics , combinatorics , invariant measure , random variable , statistics

In this paper we obtain new limit theorems for variational functionals of high frequency observations of stationary increments L\'evy driven moving averages. We will see that the asymptotic behaviour of such functionals heavily depends on the kernel, the driving L\'evy process and the properties of the functional under consideration. We show the "law of large numbers" for our class of statistics, which consists of three different cases. For one of the appearing limits, which we refer to as the ergodic type limit, we also prove the associated weak limit theory, which again consists of three different cases. Our work is related to [9,10], who considered power variation functionals of stationary increments L\'evy driven moving averages.

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