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February 2018 Noise-indicator nonnegative integer-valued autoregressive time series of the first order
Vladica Stojanović, Dragan Randjelović, Kristijan Kuk
Braz. J. Probab. Stat. 32(1): 147-171 (February 2018). DOI: 10.1214/16-BJPS335


This paper presents a modification and, at the same time, a generalization of the linear first order nonnegative integer-valued autoregressive processes, well-known as INAR(1) processes. By using the so-called Noise-Indicator, a nonlinear model with the threshold regime and with more complex structure than the appropriate linear models was obtained. The new model, named NIINAR(1) process, has been investigated in terms of the most general, the power series distribution of its innovations. Basic stochastic properties of the NIINAR(1) model (e.g., correlation structure, over-dispersion conditions and distributional properties) are given. Also, besides of some standard parameters estimators, a novel estimation techniques, together with the asymptotic properties of the obtained estimates is described. At last, a Monte Carlo study of this process is also given, as well as its application in the analysis of dynamics of two empirical dataset.


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Vladica Stojanović. Dragan Randjelović. Kristijan Kuk. "Noise-indicator nonnegative integer-valued autoregressive time series of the first order." Braz. J. Probab. Stat. 32 (1) 147 - 171, February 2018.


Received: 1 January 2016; Accepted: 1 September 2016; Published: February 2018
First available in Project Euclid: 3 March 2018

zbMATH: 06973952
MathSciNet: MR3770867
Digital Object Identifier: 10.1214/16-BJPS335

Keywords: NIINAR(1) process , Noise-indicator , parameters estimation , power series distribution

Rights: Copyright © 2018 Brazilian Statistical Association


Vol.32 • No. 1 • February 2018
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