Limit Theorems for Partial Sum Processes of Moving Averages Based on Heterogeneous Processes

Abstract

A class of partial sum processes based on a sequence of observations having the structure of finite-order moving averages is studied. The random component of this sequence is formed using a heterogeneous process in discrete time, while the non-random component is formed using a regularly varying function at infinity. The heterogeneous process with discrete time is defined as a power transform of partial sums of a certain stationary sequence. An approximation of the random processes from the above-mentioned class is studied by random processes defined as the convolution of a power transform of the fractional Brownian motion with a power function. Sufficient conditions for \(C\)-convergence in the Donsker invariance principle are obtained.