Limit theory for a class of non-stationary linear processes with weakly dependent heavy-tailed innovations

Abstract

For a class of non-stationary linear processes $(X_n{)}_n$ with weakly dependent heavy-tailed innovations we prove a convergence result for the space-time point processes $N_n={\sum }_{i=1}^n{\delta }_{(i/n,X_i/a_n)}$. Using this result and the continuous mapping theorem we then derive functional convergence of the corresponding partial maxima process in the space of càdlàg functions on $[0,1]$.