2022/09/12 by Paulauskas, Vygantas
#60F17 #60G22 #60G99 #FOS: Mathematics #Probability (math.PR)
paper · doi:10.48550/arxiv.2209.05276
In the paper we consider the partial sum process ∑k=1[nt]Xk(n), where \Xk(n)=∑j=0∞ aj(n)ξk-j(b(n)), k∈ \bz\, n≥ 1, is a series of linear processes with tapered filter aj(n)=aj\ind[0≤ j≤ ł(n)] and heavy-tailed tapered innovations ξj(b(n), j∈ \bz. Both tapering parameters b(n) and ł(n) grow to ∞ as n→ ∞. The limit behavior of the partial sum process (in the sense of convergence of finite dimensional distributions) depends on the growth of these two tapering parameters and dependence properties of a linear process with non-tapered filter ai, i≥ 0 and non-tapered innovations. We consider the cases where b(n) grows relatively slow (soft tapering) and rapidly (hard tapering), and all three cases of growth of ł(n) (strong, weak, and moderate tapering).