Zero-and-One Integer-Valued AR(1) Time Series with Power Series Innovations and Probability Generating Function Estimation Approach
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, non-negative, integer-valued autoregressive processes with zero-and-one inflated innovations, abbr. ZOINAR(1) processes...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-04-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/8/1772 |
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| author | Vladica S. Stojanović Hassan S. Bakouch Eugen Ljajko Najla Qarmalah |
| author_facet | Vladica S. Stojanović Hassan S. Bakouch Eugen Ljajko Najla Qarmalah |
| author_sort | Vladica S. Stojanović |
| collection | DOAJ |
| description | 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, non-negative, 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 probability-generating 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. |
| first_indexed | 2024-03-11T04:48:05Z |
| format | Article |
| id | doaj.art-e14c0a89e46247f88dcda88687d2ef2d |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T04:48:05Z |
| publishDate | 2023-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-e14c0a89e46247f88dcda88687d2ef2d2023-11-17T20:16:10ZengMDPI AGMathematics2227-73902023-04-01118177210.3390/math11081772Zero-and-One Integer-Valued AR(1) Time Series with Power Series Innovations and Probability Generating Function Estimation ApproachVladica S. Stojanović0Hassan S. Bakouch1Eugen Ljajko2Najla Qarmalah3Department of Informatics & Computer Sciences, University of Criminal Investigation and Police Studies, 11060 Belgrade, SerbiaDepartment of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi ArabiaDepartment of Mathematics, Faculty of Sciences & Mathematics, University of Kosovska Mitrovica, 38220 Kosovska Mitrovica, SerbiaDepartment of Mathematical Sciences, Princess Nourah bint Abdulrahman University, Riyadh 11671, Saudi ArabiaZero-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, non-negative, 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 probability-generating 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.https://www.mdpi.com/2227-7390/11/8/1772time serieszero-and-one inflationprobability generating functionsparameter estimationsimulationCOVID-19 |
| spellingShingle | Vladica S. Stojanović Hassan S. Bakouch Eugen Ljajko Najla Qarmalah Zero-and-One Integer-Valued AR(1) Time Series with Power Series Innovations and Probability Generating Function Estimation Approach Mathematics time series zero-and-one inflation probability generating functions parameter estimation simulation COVID-19 |
| title | Zero-and-One Integer-Valued AR(1) Time Series with Power Series Innovations and Probability Generating Function Estimation Approach |
| title_full | Zero-and-One Integer-Valued AR(1) Time Series with Power Series Innovations and Probability Generating Function Estimation Approach |
| title_fullStr | Zero-and-One Integer-Valued AR(1) Time Series with Power Series Innovations and Probability Generating Function Estimation Approach |
| title_full_unstemmed | Zero-and-One Integer-Valued AR(1) Time Series with Power Series Innovations and Probability Generating Function Estimation Approach |
| title_short | Zero-and-One Integer-Valued AR(1) Time Series with Power Series Innovations and Probability Generating Function Estimation Approach |
| title_sort | zero and one integer valued ar 1 time series with power series innovations and probability generating function estimation approach |
| topic | time series zero-and-one inflation probability generating functions parameter estimation simulation COVID-19 |
| url | https://www.mdpi.com/2227-7390/11/8/1772 |
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