A periodic and seasonal statistical model for non-negative integer-valued time series with an application to dispensed medications in respiratory diseases
•A new counting time series model is proposed.•The model has a periodic and seasonal autoregressive structure.•The conditional quasi-maximum likelihood method is used to estimate the parameters.•The consistency and asymptotic normality of the estimators are fully established.•Simulations and an appl...
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| Published in | Applied Mathematical Modelling Vol. 96; pp. 545 - 558 |
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| Main Authors | , , , , , |
| Format | Journal Article |
| Language | English |
| Published |
New York
Elsevier Inc
01.08.2021
Elsevier BV Elsevier |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0307-904X 1088-8691 0307-904X 1872-8480 |
| DOI | 10.1016/j.apm.2021.03.025 |
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| Abstract | •A new counting time series model is proposed.•The model has a periodic and seasonal autoregressive structure.•The conditional quasi-maximum likelihood method is used to estimate the parameters.•The consistency and asymptotic normality of the estimators are fully established.•Simulations and an application are discussed.
This paper introduces a new class of models for non-negative integer-valued time series with a periodic and seasonal autoregressive structure. Some properties of the model are discussed and the conditional quasi-maximum likelihood method is used to estimate the parameters. The consistency and asymptotic normality of the estimators are established. Their performances are investigated for finite sample sizes and the empirical results indicate that the method gives accurate estimates. The proposed model is applied to analyse the daily number of antibiotic dispensing medication for the treatment of respiratory diseases, registered in a health center of Vitória, Brazil. |
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| AbstractList | This paper introduces a new class of models for non-negative integer-valued time series with a periodic and seasonal autoregressive structure. Some properties of the model are discussed and the conditional quasi-maximum likelihood method is used to estimate the parameters. The consistency and asymptotic normality of the estimators are established. Their performances are investigated for finite sample sizes and the empirical results indicate that the method gives accurate estimates. The proposed model is applied to analyse the daily number of antibiotic dispensing medication for the treatment of respiratory diseases, registered in a health center of Vitória, Brazil. •A new counting time series model is proposed.•The model has a periodic and seasonal autoregressive structure.•The conditional quasi-maximum likelihood method is used to estimate the parameters.•The consistency and asymptotic normality of the estimators are fully established.•Simulations and an application are discussed. This paper introduces a new class of models for non-negative integer-valued time series with a periodic and seasonal autoregressive structure. Some properties of the model are discussed and the conditional quasi-maximum likelihood method is used to estimate the parameters. The consistency and asymptotic normality of the estimators are established. Their performances are investigated for finite sample sizes and the empirical results indicate that the method gives accurate estimates. The proposed model is applied to analyse the daily number of antibiotic dispensing medication for the treatment of respiratory diseases, registered in a health center of Vitória, Brazil. |
| Author | Reisen, Valderio Anselmo Bondon, Pascal Melo, Milena Machado Prezotti Filho, Paulo Roberto Ispány, Márton Sarquis Serpa, Faradiba |
| Author_xml | – sequence: 1 givenname: Paulo Roberto orcidid: 0000-0002-9332-4121 surname: Prezotti Filho fullname: Prezotti Filho, Paulo Roberto organization: Federal Institute of Espirito Santo, IFES, Brazil – sequence: 2 givenname: Valderio Anselmo orcidid: 0000-0002-8313-7648 surname: Reisen fullname: Reisen, Valderio Anselmo email: valderio.reisen@ufes.br organization: Federal University of Espirito Santo, PPGEA-CT-UFES, Brazil – sequence: 3 givenname: Pascal surname: Bondon fullname: Bondon, Pascal organization: Université Paris-Saclay, CNRS, CentraleSupélec, Laboratoire des Signaux et Systèmes, Gif-sur-Yvette, 91190, France – sequence: 4 givenname: Márton surname: Ispány fullname: Ispány, Márton organization: Faculty of Informatics, University of Debrecen, Hungary – sequence: 5 givenname: Milena Machado surname: Melo fullname: Melo, Milena Machado organization: Federal Institute of Espirito Santo, IFES, Brazil – sequence: 6 givenname: Faradiba surname: Sarquis Serpa fullname: Sarquis Serpa, Faradiba organization: EMESCAM, Brazil |
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| Cites_doi | 10.2307/3214650 10.1111/jtsa.12161 10.1111/j.1752-1688.1985.tb05379.x 10.1016/j.apm.2019.04.052 10.1111/j.1467-9892.1987.tb00438.x 10.1007/s00431-013-1958-y 10.3390/ijerph14111392 10.1136/bmjopen-2017-019315 10.1080/00949655.2019.1685995 10.1016/j.jmva.2010.05.006 10.1016/j.apm.2020.02.001 10.1080/00949655.2015.1015127 10.1016/j.jspi.2009.12.015 10.1016/j.cam.2018.07.043 10.1002/sim.4336 10.1177/1471082X15584701 10.1214/18-BJPS421 10.1016/j.jpeds.2016.11.027 10.1111/j.1467-9892.1991.tb00073.x 10.1111/j.1467-9892.1994.tb00186.x 10.1111/1467-9892.00246 10.1214/aop/1176994950 10.1111/cea.13160 10.1016/j.sigpro.2005.06.016 10.1080/03610918.2014.994780 10.2307/1427868 |
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| Keywords | Air pollution problems Count time series Periodicity Seasonality Consistency Forecast periodicity forecast air pollution problems consistency seasonality |
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| Snippet | •A new counting time series model is proposed.•The model has a periodic and seasonal autoregressive structure.•The conditional quasi-maximum likelihood method... This paper introduces a new class of models for non-negative integer-valued time series with a periodic and seasonal autoregressive structure. Some properties... |
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| SubjectTerms | Air pollution problems Antibiotics Asymptotic methods Consistency Count time series Empirical analysis Forecast Integers Maximum likelihood method Normality Parameter estimation Periodicity Respiratory diseases Seasonality Statistical models Statistics Statistics Theory Time series |
| Title | A periodic and seasonal statistical model for non-negative integer-valued time series with an application to dispensed medications in respiratory diseases |
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