Limit theorems for aggregated linear processes

Johannes Moritz Jirak

doi:10.1239/aap/1370870128

Limit theorems for aggregated linear processes

Johannes Moritz Jirak

Institute of Statistics (5060)

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	520-544
Journal	Advances in Applied Probability
Volume	45
Issue number	2
DOIs	https://doi.org/10.1239/aap/1370870128
Publication status	Published - 2013

Fields of Expertise

Information, Communication & Computing

Treatment code (Nähere Zuordnung)

Basic - Fundamental (Grundlagenforschung)

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10.1239/aap/1370870128

Asymptotic and Statistical Analysis of Time Series in Economy and Finance
Schauer, J. (Attendee), Berkes, I. (Project manager), Hörmann, S. (Other function) & Jirak, J. M. (Attendee)
1/01/02 → 31/12/24
Project: Research area

Cite this

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title = "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 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 {\textquoteleft}limiting long- or short-memory{\textquoteright} condition on the underlying linear process.",

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AB - 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.

U2 - 10.1239/aap/1370870128

DO - 10.1239/aap/1370870128

M3 - Article

SN - 1475-6064

VL - 45

SP - 520

EP - 544

JO - Advances in Applied Probability

JF - Advances in Applied Probability

IS - 2

ER -

Limit theorems for aggregated linear processes

Abstract

Fields of Expertise

Treatment code (Nähere Zuordnung)

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Projects

Asymptotic and Statistical Analysis of Time Series in Economy and Finance

Cite this