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In this paper we present some new limit theorems for power variations ofstationary increment L\'{e}vy driven moving average processes. Recently, suchasymptotic results have been investigated in [Ann. Probab. 45(6B) (2017),4477--4528, Festschrift for Bernt {\O}ksendal, Stochastics 81(1) (2017),360--383] under the assumption that the kernel function potentially exhibits asingular behaviour at $0$. The aim of this work is to demonstrate how some ofthe 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 Browniansemi-stationary models.

A limit theorem for a class of stationary increments L\'{e}vy moving average process with multiple singularities