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Random environment integer‐valued autoregressive process
Author(s) -
Nastić Aleksandar S.,
Laketa Petra N.,
Ristić Miroslav M.
Publication year - 2016
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/jtsa.12161
Subject(s) - autoregressive model , mathematics , estimator , integer (computer science) , consistency (knowledge bases) , conditional variance , negative binomial distribution , parameterized complexity , counting process , star model , variance (accounting) , conditional expectation , binomial (polynomial) , statistics , econometrics , discrete mathematics , algorithm , autoregressive integrated moving average , time series , computer science , autoregressive conditional heteroskedasticity , poisson distribution , volatility (finance) , accounting , business , programming language
An r states random environment integer‐valued autoregressive process of order 1, RrINAR(1), is introduced. Also, a random environment process is separately defined as a selection mechanism of differently parameterized geometric distributions, thus ensuring the non‐stationary nature of the RrNGINAR(1) model based on the negative binomial thinning. The distributional and correlation properties of this model are discussed, and the k ‐step‐ahead conditional expectation and variance are derived. Yule–Walker estimators of model parameters are presented and their strong consistency is proved. The RrNGINAR(1) model motivation is justified on simulated samples and by its application to specific real‐life counting data.