Statistical Modelling 6 (2006), 81–96
Binomial thinning models for integer time series
Robert C Jung
Universität Tübingen,
Wirtschaftswissenschaftliche Fakultät,
Mohlstr. 36,
D–72074 Tübingen
Germany
eMail: robert.jung@uni-tuebingen.de
A.R. Tremayne
University of Sidney, Sidney, Australia
and
University of York, York, UK
Abstract:
This article considers some simple observation-driven time series
models for counts.We provide
a brief description of the class of integer-valued autoregressive
(INAR) and integer-valued moving average
(INMA) processes. These classes of models may be attractive when
the data exhibit a significant serial
dependence structure.We, therefore, briefly reviewvarious testing
procedures useful for assessing the serial
correlation in the data. Once it is established that the data are
not serially independent, suitable INAR
or INMA processes may be employed to model the data. In the
important first order INAR model, we
discuss various methods of estimating the structural parameters
of the process.We also give a short account
of the extension of some of these estimation procedures to second
order INAR models. Moving average
counterparts of both models are also entertained. Throughout, the
models and methods are illustrated in
the context of a famous data set from the branching process
literature that turns out to be surprisingly
difficult to model satisfactorily.
Keywords:
time series of counts; INAR and INMA models;
parameter estimates; assessing dependence
Downloads:
Example
data
(taken from
Fürth, Reinhold: Statistik und Wahrscheinlichkeitsnachwirkung.
Physikalische Zeitschrift 19 (1918) 421–426)
in zipped archive
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