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Difference Equations for the Higher Order Moments and Cumulants of the INAR( p ) Model
Author(s) -
Silva Maria Eduarda,
Oliveira Vera Lúcia
Publication year - 2005
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/j.1467-9892.2005.00388.x
Subject(s) - mathematics , cumulant , autoregressive model , bilinear interpolation , series (stratigraphy) , mathematical analysis , statistics , paleontology , biology
. Here we obtain difference equations for the higher order moments and cumulants of a time series { X t } 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 method – the 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 patient.