The max-BARMA models for counts with bounded support

In this note, we introduce a discrete counterpart of the conventional max-autoregressive moving-average process of Davis and Resnick (1989), based on the binomial thinning operator and driven by a sequence of i. i. d. nonnegative integer-valued random variables with a finite range of counts. Basic p...

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Bibliographic Details
Published in:	Statistics & probability letters Vol. 143; pp. 28 - 36
Main Authors:	Weiß, Christian H., Scotto, Manuel G., Möller, Tobias A., Gouveia, Sónia
Format:	Journal Article
Language:	English
Published:	Elsevier B.V 01.12.2018
Subjects:	Autoregressive moving-average processes Finite counts Thinning operator Autoregressive moving-average processes Finite counts Thinning operator
ISSN:	0167-7152, 1879-2103
Online Access:	Get full text
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Summary:	In this note, we introduce a discrete counterpart of the conventional max-autoregressive moving-average process of Davis and Resnick (1989), based on the binomial thinning operator and driven by a sequence of i. i. d. nonnegative integer-valued random variables with a finite range of counts. Basic probabilistic and statistical properties of this new class of models are discussed in detail, namely the existence of a stationary distribution, and how observations’ and innovations’ distributions are related to each other. Furthermore, parameter estimation is also addressed.
ISSN:	0167-7152 1879-2103
DOI:	10.1016/j.spl.2018.07.011