A limit theorem for a class of stationary increments Lévy moving average process with multiple singularities

Mathias Mørck Ljungdahl; Mark Podolskij

doi:10.15559/18-VMSTA111

paper

A limit theorem for a class of stationary increments Lévy moving average process with multiple singularities

arXiv:1803.01017 · doi:10.15559/18-VMSTA111

Abstract

In this paper we present some new limit theorems for power variations of stationary increment Lévy driven moving average processes. Recently, such asymptotic results have been investigated in [Ann. Probab. 45(6B) (2017), 4477--4528, Festschrift for Bernt Øksendal, Stochastics 81(1) (2017), 360--383] under the assumption that the kernel function potentially exhibits a singular behaviour at $0$ . The aim of this work is to demonstrate how some of the results change when the kernel function has multiple singularity points. Our paper is also related to the article [Stoch. Process. Appl. 125(2) (2014), 653--677] that studied the same mathematical question for the class of Brownian semi-stationary models.

Published at https://doi.org/10.15559/18-VMSTA111 in the Modern Stochastics: Theory and Applications (https://www.i-journals.org/vtxpp/VMSTA) by VTeX (http://www.vtex.lt/)