Difference Equations for the Higher‐Order Moments and Cumulants of the INAR(1) Model

Maria Eduarda Da Silva and Vera Lúcia Oliveira

Journal of Time Series Analysis, 2004, vol. 25, issue 3, 317-333

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.

Date: 2004
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https://doi.org/10.1111/j.1467-9892.2004.01685.x

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