LIMIT THEOREMS FOR AGGREGATED LINEAR PROCESSES

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 {Y-1((N)),...,Y-n((N))} of the normalized N-fold aggregated process, we describe the limiting behavior of statistics T-N,T-n = T-N,T-n(Y-1((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.