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Limit Theorems for Aggregated Linear Processes

Part of: Stochastic processes Limit theorems

Published online by Cambridge University Press:  22 February 2016

M. Jirak
M. Jirak*
Affiliation:
Graz University of Technology
*
∗ Current address: Institut für Mathematik, Humboldt-Universität zu Berlin, Unter den Linden 6, D-10099 Berlin, Germany.
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Abstract

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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,n = T N,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.

Keywords

Aggregationshort memorylong memoryinvariance principlerandom coefficient MA(∞)martingale decomposition

MSC classification

Primary: 60F17: Functional limit theorems; invariance principles
Secondary: 60G99: None of the above, but in this section

Information

Type
General Applied Probability
Information
Advances in Applied Probability , Volume 45 , Issue 2 , June 2013 , pp. 520 - 544
Copyright
© Applied Probability Trust 

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