Difference Equations for the Higher Order Moments and
Cumulants of the INAR(p) Model
Abstract
Here we obtain difference equations for the higher order
moments and cumulants of a time series
{Xt} satisfying an INAR(p)
model. These equations are similar to the difference
equations for the higher order moments and cumulants of the
bilinear time series model. We obtain the spectral and
bispectral density functions for the INAR(p) process in state
space form, thus characterizing it in the frequency domain.
We consider a frequency domain methot - tha Whittle criterion
- to estimate the parameters of the INAR(p) model and
illustrate it with the series of the number of epilepsy
seizures of a pacient.