  In this paper we present some new limit theorems for power variations of
stationary increment L\'{e}vy driven moving average processes. Recently, such
asymptotic 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 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.
