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Central limit theorems for nearly long range dependent subordinated linear processes

Part of: Stochastic processes Limit theorems Inference from stochastic processes

Published online by Cambridge University Press:  16 July 2020

Martin Wendler  and
Wei Biao Wu
Martin Wendler*
Affiliation:
Otto-von-Guericke-Universität Magdeburg
Wei Biao Wu*
Affiliation:
University of Chicago
*
*Postal address: Otto-von-Guericke-Universität Magdeburg, Universitätsplatz 2, 39106Magdeburg, Germany. Email: martin.wendler@ovgu.de
**Postal address: University of Chicago, 5747 South Ellis Avenue, Chicago, IL60637, USA
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Abstract

The limit behavior of partial sums for short range dependent stationary sequences (with summable autocovariances) and for long range dependent sequences (with autocovariances summing up to infinity) differs in various aspects. We prove central limit theorems for partial sums of subordinated linear processes of arbitrary power rank which are at the border of short and long range dependence.

Keywords

Central limit theoremlong range dependencelinear processespower rank

MSC classification

Primary: 60F05: Central limit and other weak theorems
Secondary: 60G10: Stationary processes 62M10: Time series, auto-correlation, regression, etc.

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 57 , Issue 2 , June 2020 , pp. 637 - 656
Copyright
© Applied Probability Trust 2020

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