Noise-indicator nonnegative integer-valued autoregressive time series of the first order
Abstract
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.
Keywords:
Noise-indicator / power series distribution / NIINAR(1) process / parameters estimationSource:
Brazilian journal of probability and statistics, 2018, 32, 1, 147-171Publisher:
- Brazilian Statistical Association, Sao Paulo
Funding / projects:
- New Information Technologies for Analytical Decision Making Based on Experiment Observation and their Application in Biological, Economic and Sociological Systems (RS-MESTD-Integrated and Interdisciplinary Research (IIR or III)-44007)
- Interdisciplinary research of Serbian cultural and linguistic heritage. Creation of multimedial Internet portal “The Lexicon of Serbian Culture” (RS-MESTD-Integrated and Interdisciplinary Research (IIR or III)-47016)
DOI: 10.1214/16-BJPS335
ISSN: 0103-0752
WoS: 000427678700007
Scopus: 2-s2.0-85045530235
Collections
Institution/Community
JakovTY - JOUR AU - Stojanović, Vladica AU - Ranđelović, Dragan AU - Kuk, Kristijan PY - 2018 UR - http://jakov.kpu.edu.rs/handle/123456789/846 AB - 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. PB - Brazilian Statistical Association, Sao Paulo T2 - Brazilian journal of probability and statistics T1 - Noise-indicator nonnegative integer-valued autoregressive time series of the first order VL - 32 IS - 1 SP - 147 EP - 171 DO - 10.1214/16-BJPS335 ER -
@article{ author = "Stojanović, Vladica and Ranđelović, Dragan and Kuk, Kristijan", year = "2018", abstract = "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.", publisher = "Brazilian Statistical Association, Sao Paulo", journal = "Brazilian journal of probability and statistics", title = "Noise-indicator nonnegative integer-valued autoregressive time series of the first order", volume = "32", number = "1", pages = "147-171", doi = "10.1214/16-BJPS335" }
Stojanović, V., Ranđelović, D.,& Kuk, K.. (2018). Noise-indicator nonnegative integer-valued autoregressive time series of the first order. in Brazilian journal of probability and statistics Brazilian Statistical Association, Sao Paulo., 32(1), 147-171. https://doi.org/10.1214/16-BJPS335
Stojanović V, Ranđelović D, Kuk K. Noise-indicator nonnegative integer-valued autoregressive time series of the first order. in Brazilian journal of probability and statistics. 2018;32(1):147-171. doi:10.1214/16-BJPS335 .
Stojanović, Vladica, Ranđelović, Dragan, Kuk, Kristijan, "Noise-indicator nonnegative integer-valued autoregressive time series of the first order" in Brazilian journal of probability and statistics, 32, no. 1 (2018):147-171, https://doi.org/10.1214/16-BJPS335 . .