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),…,Yn(N)} of the normalizedN-fold aggregated process, we describe the limiting behavior of statisticsTN,n=TN,n(Y1(N),…,Yn(N)) in both of the casesn/N(n)→ 0 andN(n)/n→ 0, assuming either a ‘limiting long- or short-memory’ condition on the underlying linear process.