2021/11/16 by Vygantas Paulauskas, Paulauskas, Vygantas
Mathematics · Economics, Econometrics and Finance · #Stochastic processes and statistical mechanics #Stochastic processes and financial applications #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.2111.08321
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 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 case where b(n) grows relatively slow (soft tapering), and all three cases of growth of ł(n) (strong, weak, and moderate tapering). In these cases the limit processes (in the sense of convergence of finite dimensional distributions) are Gaussian.