Flexible Lévy-Based Models for Time Series of Count Data with Zero-Inflation, Overdispersion, and Heavy Tails
The explosion of time series count data with diverse characteristics and features in recent years has led to a proliferation of new analysis models and methods. Significant efforts have been devoted to achieving flexibility capable of handling complex dependence structures, capturing multiple distri...
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| Format: | Article |
| Language: | English |
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Wiley
2023-01-01
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| Series: | Journal of Probability and Statistics |
| Online Access: | http://dx.doi.org/10.1155/2023/1780404 |
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| author | Confort Kollie Philip Ngare Bonface Malenje |
| author_facet | Confort Kollie Philip Ngare Bonface Malenje |
| author_sort | Confort Kollie |
| collection | DOAJ |
| description | The explosion of time series count data with diverse characteristics and features in recent years has led to a proliferation of new analysis models and methods. Significant efforts have been devoted to achieving flexibility capable of handling complex dependence structures, capturing multiple distributional characteristics simultaneously, and addressing nonstationary patterns such as trends, seasonality, or change points. However, it remains a challenge when considering them in the context of long-range dependence. The Lévy-based modeling framework offers a promising tool to meet the requirements of modern data analysis. It enables the modeling of both short-range and long-range serial correlation structures by selecting the kernel set accordingly and accommodates various marginal distributions within the class of infinitely divisible laws. We propose an extension of the basic stationary framework to capture additional marginal properties, such as heavy-tailedness, in both short-term and long-term dependencies, as well as overdispersion and zero inflation in simultaneous modeling. Statistical inference is based on composite pairwise likelihood. The model’s flexibility is illustrated through applications to rainfall data in Guinea from 2008 to 2023, and the number of NSF funding awarded to academic institutions. The proposed model demonstrates remarkable flexibility and versatility, capable of simultaneously capturing overdispersion, zero inflation, and heavy-tailedness in count time series data. |
| format | Article |
| id | doaj-art-2da2f87a22734ff4bbb1b03d96be892a |
| institution | Kabale University |
| issn | 1687-9538 |
| language | English |
| publishDate | 2023-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Probability and Statistics |
| spelling | doaj-art-2da2f87a22734ff4bbb1b03d96be892a2025-02-03T01:29:35ZengWileyJournal of Probability and Statistics1687-95382023-01-01202310.1155/2023/1780404Flexible Lévy-Based Models for Time Series of Count Data with Zero-Inflation, Overdispersion, and Heavy TailsConfort Kollie0Philip Ngare1Bonface Malenje2Pan African University Institute for Basic SciencesSchool of MathematicsJomo Kenyatta University of Agriculture and TechnologyThe explosion of time series count data with diverse characteristics and features in recent years has led to a proliferation of new analysis models and methods. Significant efforts have been devoted to achieving flexibility capable of handling complex dependence structures, capturing multiple distributional characteristics simultaneously, and addressing nonstationary patterns such as trends, seasonality, or change points. However, it remains a challenge when considering them in the context of long-range dependence. The Lévy-based modeling framework offers a promising tool to meet the requirements of modern data analysis. It enables the modeling of both short-range and long-range serial correlation structures by selecting the kernel set accordingly and accommodates various marginal distributions within the class of infinitely divisible laws. We propose an extension of the basic stationary framework to capture additional marginal properties, such as heavy-tailedness, in both short-term and long-term dependencies, as well as overdispersion and zero inflation in simultaneous modeling. Statistical inference is based on composite pairwise likelihood. The model’s flexibility is illustrated through applications to rainfall data in Guinea from 2008 to 2023, and the number of NSF funding awarded to academic institutions. The proposed model demonstrates remarkable flexibility and versatility, capable of simultaneously capturing overdispersion, zero inflation, and heavy-tailedness in count time series data.http://dx.doi.org/10.1155/2023/1780404 |
| spellingShingle | Confort Kollie Philip Ngare Bonface Malenje Flexible Lévy-Based Models for Time Series of Count Data with Zero-Inflation, Overdispersion, and Heavy Tails Journal of Probability and Statistics |
| title | Flexible Lévy-Based Models for Time Series of Count Data with Zero-Inflation, Overdispersion, and Heavy Tails |
| title_full | Flexible Lévy-Based Models for Time Series of Count Data with Zero-Inflation, Overdispersion, and Heavy Tails |
| title_fullStr | Flexible Lévy-Based Models for Time Series of Count Data with Zero-Inflation, Overdispersion, and Heavy Tails |
| title_full_unstemmed | Flexible Lévy-Based Models for Time Series of Count Data with Zero-Inflation, Overdispersion, and Heavy Tails |
| title_short | Flexible Lévy-Based Models for Time Series of Count Data with Zero-Inflation, Overdispersion, and Heavy Tails |
| title_sort | flexible levy based models for time series of count data with zero inflation overdispersion and heavy tails |
| url | http://dx.doi.org/10.1155/2023/1780404 |
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