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On two classes of reflected autoregressive processes

Part of: Special processes Inference from stochastic processes

Published online by Cambridge University Press:  16 July 2020

Onno Boxma ,
Andreas Löpker  and
Michel Mandjes
Onno Boxma*
Affiliation:
Eindhoven University of Technology
Andreas Löpker*
Affiliation:
HTW Dresden
Michel Mandjes*
Affiliation:
University of Amsterdam
*
*Postal address: Department of Mathematics and Computer Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven. Email address: o.j.boxma@tue.nl
**Postal address: University of Applied Sciences, Hochschule für Technik und Wirtschaft, Friedrich-List-Platz 1, D-01069 Dresden, Germany. Email address: lopker@htw-dresden.de
***Postal address: Korteweg-de Vries Institute for Mathematics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands. Email address: m.r.h.mandjes@uva.nl
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Abstract

We introduce two general classes of reflected autoregressive processes, INGAR+ and GAR+. Here, INGAR+ can be seen as the counterpart of INAR(1) with general thinning and reflection being imposed to keep the process non-negative; GAR+ relates to AR(1) in an analogous manner. The two processes INGAR+ and GAR+ are shown to be connected via a duality relation. We proceed by presenting a detailed analysis of the time-dependent and stationary behavior of the INGAR+ process, and then exploit the duality relation to obtain the time-dependent and stationary behavior of the GAR+ process.

Keywords

INAR(1)AR(1)autoregressive processesreflectiongenerating functionstime-dependent behaviorstationarity

MSC classification

Primary: 60K10: Applications (reliability, demand theory, etc.)
Secondary: 62M10: Time series, auto-correlation, regression, etc. 60K25: Queueing theory
Type
Research Papers
Information
Journal of Applied Probability , Volume 57 , Issue 2 , June 2020 , pp. 657 - 678
Copyright
© Applied Probability Trust 2020

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