Difference Equations for the Higher Order Moments and Cumulants
of the INAR(1) Model
Abstract
Recently, as a result of the growing interest in modelling
stationary processes with discrete marginal distributions,
several models for integer value time series have been proposed
in the literature. One of these models is the
INteger-AutoRegressive (INAR) model. Here we
consider the higher order moments and cumulants of the
INAR(1) process and show that they satisfy a set of
Yule-Walker type difference equations. We also obtain the
spectral and bispectral density functions, thus characterizing
the INAR(1) process in the frequency domain. We use a
frequency domain approach, namely the Whittle criterion, to
estimate the parameters of the model. The estimation theory and
associated asymptotic theory of this estimation method are
illustrated numerically.