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First‐order rounded integer‐valued autoregressive (RINAR(1)) process
Author(s) -
Kachour M.,
Yao J. F.
Publication year - 2009
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.1467-9892.2009.00620.x
Subject(s) - mathematics , autoregressive model , star model , ergodicity , identifiability , autocorrelation , series (stratigraphy) , estimator , moving average model , integer (computer science) , nonlinear autoregressive exogenous model , time series , mathematical optimization , econometrics , statistics , autoregressive integrated moving average , computer science , paleontology , biology , programming language
. We introduce a new class of autoregressive models for integer‐valued time series using the rounding operator. Compared with classical INAR models based on the thinning operator, the new models have several advantages: simple innovation structure, autoregressive coefficients with arbitrary signs, possible negative values for time series and possible negative values for the autocorrelation function. Focused on the first‐order RINAR(1) model, we give conditions for its ergodicity and stationarity. For parameter estimation, a least squares estimator is introduced and we prove its consistency under suitable identifiability condition. Simulation experiments as well as analysis of real data sets are carried out to attest the model performance.