TY  - JOUR
AU  - Stojanović, Vladica S.
AU  - Bakouch, Hassan S.
AU  - Ljajko, Eugen
AU  - Qarmalah, Najla
PY  - 2023
UR  - https://jakov.kpu.edu.rs/handle/123456789/1632
AB  - Zero-and-one inflated count time series have only recently become the subject of more extensive interest and research. One of the possible approaches is represented by first-order, nonnegative, integer-valued autoregressive processes with zero-and-one inflated innovations, abbr. ZOINAR(1) processes, introduced recently, around the year 2020 to the present. This manuscript presents a generalization of ZOINAR processes, given by introducing the zero-and-one inflated power series (ZOIPS) distributions. Thus, the obtained process, named the ZOIPS-INAR(1) process, has been investigated in terms of its basic stochastic properties (e.g., moments, correlation structure and distributional properties). To estimate the parameters of the ZOIPS-INAR(1) model, in addition to the conditional least-squares (CLS) method, a recent estimation technique based on probabilitygenerating functions (PGFs) is discussed. The asymptotic properties of the obtained estimators are also examined, as well as their Monte Carlo simulation study. Finally, as an application of the ZOIPS-INAR(1) model, a dynamic analysis of the number of deaths from the disease COVID-19 in Serbia is considered.
PB  - Basel : MDPI
T2  - Mathematics
T1  - Zero-and-One Integer-Valued AR(1) Time Series with Power Series Innovations and Probability Generating Function Estimation Approach
VL  - 11
IS  - 8
SP  - 1772
DO  - 10.3390/math11081772
ER  - 

@article{
author = "Stojanović, Vladica S. and Bakouch, Hassan S. and Ljajko, Eugen and Qarmalah, Najla",
year = "2023",
abstract = "Zero-and-one inflated count time series have only recently become the subject of more extensive interest and research. One of the possible approaches is represented by first-order, nonnegative, integer-valued autoregressive processes with zero-and-one inflated innovations, abbr. ZOINAR(1) processes, introduced recently, around the year 2020 to the present. This manuscript presents a generalization of ZOINAR processes, given by introducing the zero-and-one inflated power series (ZOIPS) distributions. Thus, the obtained process, named the ZOIPS-INAR(1) process, has been investigated in terms of its basic stochastic properties (e.g., moments, correlation structure and distributional properties). To estimate the parameters of the ZOIPS-INAR(1) model, in addition to the conditional least-squares (CLS) method, a recent estimation technique based on probabilitygenerating functions (PGFs) is discussed. The asymptotic properties of the obtained estimators are also examined, as well as their Monte Carlo simulation study. Finally, as an application of the ZOIPS-INAR(1) model, a dynamic analysis of the number of deaths from the disease COVID-19 in Serbia is considered.",
publisher = "Basel : MDPI",
journal = "Mathematics",
title = "Zero-and-One Integer-Valued AR(1) Time Series with Power Series Innovations and Probability Generating Function Estimation Approach",
volume = "11",
number = "8",
pages = "1772",
doi = "10.3390/math11081772"
}

Stojanović, V. S., Bakouch, H. S., Ljajko, E.,& Qarmalah, N.. (2023). Zero-and-One Integer-Valued AR(1) Time Series with Power Series Innovations and Probability Generating Function Estimation Approach. in Mathematics
Basel : MDPI., 11(8), 1772.
https://doi.org/10.3390/math11081772

Stojanović VS, Bakouch HS, Ljajko E, Qarmalah N. Zero-and-One Integer-Valued AR(1) Time Series with Power Series Innovations and Probability Generating Function Estimation Approach. in Mathematics. 2023;11(8):1772.
doi:10.3390/math11081772 .

Stojanović, Vladica S., Bakouch, Hassan S., Ljajko, Eugen, Qarmalah, Najla, "Zero-and-One Integer-Valued AR(1) Time Series with Power Series Innovations and Probability Generating Function Estimation Approach" in Mathematics, 11, no. 8 (2023):1772,
https://doi.org/10.3390/math11081772 . .