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 normalized N-fold aggregated process, we describe the limiting behavior of statistics TN,n= TN,n(Y1(N),..., Yn(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.
Citation
M. Jirak. "Limit theorems for aggregated linear processes." Adv. in Appl. Probab. 45 (2) 520 - 544, June 2013. https://doi.org/10.1239/aap/1370870128
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