Premium
Existence and Stochastic Structure of a Non‐negative Integer‐valued Autoregressive Process
Author(s) -
Latour Alain
Publication year - 1998
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 - 10.1111/1467-9892.00102
Subject(s) - autoregressive model , mathematics , star model , integer (computer science) , simple (philosophy) , representation (politics) , stochastic process , econometrics , statistics , autoregressive integrated moving average , time series , computer science , law , programming language , philosophy , epistemology , politics , political science
A simple criterion is given for the existence of a generalized integer‐valued autoregressive (GINAR( p )) process. We show that the GINAR( p ) process is nothing but an AR( p ) process. The spectral density gives a good insight into the stochastic structure of a GINAR( p ) model. The spectral representation of the process is explicitly given. The estimation of parameters of the process is also discussed and clarifies some results presented by Du and Li (The integer‐valued autoregressive (INAR( p )) model. J. Times Ser. Anal. , 12 (1991), 129‐‐42). Finally, we describe the number of seizures of an epileptic patient using a model of this class.