 
Summary: DISCRETE VARIATE TIME SERIES
Eddie McKenzie
Department of Statistics & Modelling Science
University of Strathclyde
15th August 2000
1 Introduction
Modelling discrete variate time series is the most challenging and, as yet, least well
developed of all areas of research in time series. The fact that variate values are integer
renders most traditional representations of dependence either impossible or impractical.
In the last two decades there have been a number of imaginative attempts to develop a
suitable class of models. Our purpose here is to briefly review some of the most interesting
and exciting of these.
Discrete variate time series occur in many contexts, often as counts of events, objects
or individuals in consecutive intervals or at consecutive points in time. Some simple
examples are the numbers of accidents in a manufacturing plant each month, the numbers
of patients treated by a hospital's accident and emergency unit each hour, the numbers of
fish caught in a particular area of sea each week, the numbers of busy lines in a telephone
network noted every thirty minutes, and the numbers of lifts in a tall office building which
are fully operational at the start of business each day. Such data may also arise from the
discretization of continuous variate time series. An example of this is the reduction of
