Limit theorems for aggregated linear processes

Abstract

In this paper we develop an asymptotic theory of aggregated linear processes, and determine in particular the limit distribution of a large class of linear and nonlinear functionals of such processes. Given a sample {Y₁^(N),...,Y_n^(N)} of the normalized N-fold aggregated process, we describe the limiting behavior of statistics T_N,n= T_N,n(Y₁^(N),..., Y_n^(N)) in both of the cases n/N(n) → 0 and N(n)/n → 0, assuming either a `limiting long- or short-memory' condition on the underlying linear process.