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Integer-valued Autoregressive Model Based on Innovations with Discrete Exponential-Weibull Distribution
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Einolah Deiri    , Einolah Deiri * , Ezzatallah Jamkhaneh |
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Abstract: (2960 Views) |
| In this paper, a new integer-valued autoregressive process is introduced based on the discrete exponential-Weibull distribution to model integer-value time series data. Regarding the importance of discrete distributions in counting data modeling, the discrete counterpart of the exponential-Weibull distribution is introduced, and some of its statistical properties, such as survival function, hazard rate, moment generating function, skewness and kurtosis, are investigated. The Fisher dispersion, skewness and kurtosis indices show the flexibility and efficiency of the discrete Exponential-Weibull distribution in fitting different types of counting data. The discrete Exponential-Weibull distribution covers data fits with different dispersion characteristics (overdispersion, underdispersion and equidispersion), long right tail (skewed to the right) and heavy-tailed. The model parameters are estimated using three approaches maximum conditional likelihood, minimum generalized conditional squares, and Yule-Walker. Finally, the efficiency and superiority of the process in fitting counts data of deaths due to COVID-19 disease are compared with other competing models. |
Article number: 12 |
| Keywords: INAR(1) process, Discrete Exponential-Weibull, Dispersion index, Heavy-tailed. |
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Full-Text [PDF 227 kb]
(2446 Downloads)
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Type of Study: Applied |
Subject:
Time Series
Received: 2022/01/9 | Accepted: 2023/03/1 | Published: 2022/12/21
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1. Alizadeh, M., Altun, E., Cordeiro, G.M. and Rasekhi M. (2017), The Odd Power Cauchy Family of Distributions: Properties, Regression Models and Applications, Journal of Statistical Computation and Simulation, 88(4), 785-807. [ DOI:10.1080/00949655.2017.1406938] 2. Al-Osh, M.A. and Aly, E.E.A.A. (1992), First Order Autoregressive Time Series with Negative Binomial and Geometric Marginals, Communications in Statistics-Theory and Methods, 21, 2483-2492. [ DOI:10.1080/03610929208830925] 3. Al-Osh, M.A. and Alzaid, A.A. (1987), First-order Integer-valued Autoregressive (INAR(1)) Process, Journal of Time Series Analysis, 8, 261-275. [ DOI:10.1111/j.1467-9892.1987.tb00438.x] 4. Altun, E., El-Morshedy, E. and Eliwa E.S. (2020), A Study on Discrete Bilal Distribution with Properties and Applications on Integer-valued Autoregressive Process, Revstat-Statistical Journal, 20, 501-528. 5. Alzaid, A.A. and Al-Osh, M.A. (1988), First-order Integer-valued Autoregressive (INAR(1)) Process: Distributional and Regression Properties, Statistica Neerlandica, 42, 53-61. [ DOI:10.1111/j.1467-9574.1988.tb01521.x] 6. Amini, M. and Roozbeh, M. (2015), Optimal Partial Ridge Estimation in Restricted Semiparametric Regression Models, Journal of Multivariate Analysis, 136, 26-40. [ DOI:10.1016/j.jmva.2015.01.005] 7. Borges, P., Bourguignon, M. and Molinares, F.F. (2017), A Generalized NGINAR(1) Process with Inflated Parameter Geometric Counting Series, Australian & New Zealand Journal of Statistics, 59, 137-150. [ DOI:10.1111/anzs.12184] 8. Eliwa, M.S., Altun, E., El-Dawoody, M. and El-Morshedy, M. (2020), A New Three-parameter Discrete Distribution with Associated INAR(1) Process and Applications, IEEE Access, 8, 91150-91162. [ DOI:10.1109/ACCESS.2020.2993593] 9. Eliwa, M.S. and El-Morshedy, M. (2022), A One-parameter Discrete Distribution for Over-dispersed Data: Statistical and Reliability Properties with Applications, Journal of Applied Statistics, 49, 2467-2487. [ DOI:10.1080/02664763.2021.1905787] [ PMID] [ ] 10. El-Morshedy, M., Eliwa, M.S. and Altun, E. (2020), Discrete Burr-Hatke Distribution with Properties, Estimation Methods and Regression Model, IEEE Access, 8, 74359-74370. [ DOI:10.1109/ACCESS.2020.2988431] 11. Marques, P.C.F., Graziadei, H. and Lopes, H.F. (2022), Bayesian Generalizations of the Integer-valued Autoregressive Model, Journal of Applied Statistics, 49(2), 336-356. [ DOI:10.1080/02664763.2020.1812544] [ PMID] [ ] 12. Gómez-Déniz, E. and Calderín-Ojeda, E. (2011), The Discrete Lindley Distribution: Properties and Applications, Journal of Statistical Computation and Simulation, 81(11), 1405-1416. [ DOI:10.1080/00949655.2010.487825] 13. Huang, J. and Zhu, F. (2021), A New First-order Integer-valued Autoregressive Model with Bell Innovations, Entropy, 323, 713. [ DOI:10.3390/e23060713] [ PMID] [ ] 14. Irshad, M.R., Chesneau, C., D'cruz, V. and Maya, R. (2021), Discrete Pseudo Lindley Distribution: Properties, Estimation and Application on INAR(1) Process, Mathematical and Computational Applications, 26(4), 76. [ DOI:10.3390/mca26040076] 15. Karlsen, H. and Tjøstheim, D. (1988), Consistent Estimates for the NEAR(2) and NLAR(2) Time Series Models, Journal of the Royal Statistical Society. Series B (Methodological), 50(2), 313-320. [ DOI:10.1111/j.2517-6161.1988.tb01730.x] 16. Krishna, H. and Pundir, P.S. (2009), Discrete Burr and Discrete Pareto Distributions, Statistical Methodology, 6, 177-188. [ DOI:10.1016/j.stamet.2008.07.001] 17. Liu, Z. and Zhu, F. (2021), A New Extension of Thinning-based Integer-valued Autoregressive Models for Count Data, Entropy, 23(1), 62. [ DOI:10.3390/e23010062] [ PMID] [ ] 18. Lívio, T., Mamode Khan, N., Bourguignon, M. and Bakouch, S.H. (2018), An INAR(1) Model with Poisson-Lindley Innovations, Economics Bulletin, 38(3), 1505-1513. 19. McKenzie, E. (1986), Autoregressive Moving-average Processes with Negative Binomial and Geometric Distributions, Advances in Applied Probability, 18, 679-705. [ DOI:10.2307/1427183] 20. Miletić Ilić, A.V. (2016), A Geometric Time Series Model with a New Dependent Bernoulli Counting Series, Communications in Statistics-Theory and Methods, 45, 6400-6415. [ DOI:10.1080/03610926.2014.895840] 21. Mohammadpour, M. and Shirozhan M. (2020), An INAR(1) Model Based on Negative Binomial Thinning Operator with Serially Dependent Noise, Journal of Statistical Sciences, 14(1), 215-232. [ DOI:10.29252/jss.14.1.217] 22. Nakagawa, T. and Osaki, S. (1975), Discrete Weibull distribution, IEEE Transaction on Reliability, 24, 300-301. [ DOI:10.1109/TR.1975.5214915] 23. Nastić, A.S., Ristić, M.M. and Miletić Ilić, A.V. (2017), A Geometric Time Series Model with an Alternative Dependent Bernoulli Counting Series, Communications in Statistics-Theory and Methods, 46(2), 770-785. [ DOI:10.1080/03610926.2015.1005100] 24. Ristić, M.M., Bakouch, H.S. and Nastić, A.S. (2009), A New Geometric First-order Integer-valued Autoregressive (NGINAR(1)) Process, Journal of Statistical Planning and Inference, 139, 2218-2226. [ DOI:10.1016/j.jspi.2008.10.007] 25. Ristić, M.M., Nastić, S.A. and Miletić Ilić, V.A. (2013), A Geometric Time Series Model with Dependent Bernoulli Counting Series, Journal of Time Series Analysis, 34(4), 423-516. [ DOI:10.1111/jtsa.12023] 26. Roozbeh, M. (2018), Optimal QR-based Estimation in Partially Linear Regression Models with Correlated Errors Using GCV Criterion, Computational Statistics and Data Analysis, 117, 45-61. [ DOI:10.1016/j.csda.2017.08.002] 27. Shamma, N., Mohammadpour, M. and Shirozhan, M. (2020), A Time Series Model based on Dependent Zero Inflated Counting Series, Computational statistics, 35, 1737-1757. [ DOI:10.1007/s00180-020-00982-4] 28. Weiß, C.H. (2008), Thinning Operations for Modeling Time Series of Count-a Survey, AStA Advances in Statistical Analysis, 92, 319-341. [ DOI:10.1007/s10182-008-0072-3] 29. Weiß, C.H. (2018), An Introduction to Discrete‐Valued Time Series, John Wiley & Sons Ltd. [ DOI:10.1002/9781119097013] |
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