{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,11,27]],"date-time":"2024-11-27T21:40:16Z","timestamp":1732743616796,"version":"3.29.0"},"reference-count":29,"publisher":"Walter de Gruyter GmbH","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2024,12,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>In this paper, we introduce a class of periodic integer-valued autoregressive BL-PINAR(1) models with Bell innovations distribution based on the binomial thinning operator.\nThe basic probabilistic and statistical properties of this class are studied.\nIndeed, the first and the second moment periodically stationary conditions are established.\nThe closed forms of these moments are, under the obtained conditions, derived.\nFurthermore, the periodic autocovariance structure is also considered while providing the closed form of the periodic autocorrelation function.\nThe conditional least squares (CLS), Yule\u2013Walker (YW), weighted conditional least squares (WCLS), and conditional maximum likelihood (CML) methods are applied to estimate the underlying parameters.\nThe asymptotic properties of the CLS and the YW estimators are obtained.\nThe performances of these methods are compared through a simulation study.\nAn application on a real data set is provided.<\/jats:p>","DOI":"10.1515\/mcma-2024-2015","type":"journal-article","created":{"date-parts":[[2024,9,25]],"date-time":"2024-09-25T14:59:45Z","timestamp":1727276385000},"page":"413-430","source":"Crossref","is-referenced-by-count":0,"title":["Periodic INAR(1) model with Bell innovations distribution"],"prefix":"10.1515","volume":"30","author":[{"given":"Abderrahmen","family":"Manaa","sequence":"first","affiliation":[{"name":"Higher National School of Biotechnology Taoufik Khaznadar , Nouveau P\u00f4le Universitaire Ali Mendjeli , BP. E66 , Constantine 25100 , Algeria"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2024,9,26]]},"reference":[{"key":"2024112721095514671_j_mcma-2024-2015_ref_001","doi-asserted-by":"crossref","unstructured":"M. A. Al-Osh and A. A. Alzaid,\nFirst-order integer-valued autoregressive (INAR(1)) process,\nJ. Time Ser. Anal. 8 (1987), no. 3, 261\u2013275.","DOI":"10.1111\/j.1467-9892.1987.tb00438.x"},{"key":"2024112721095514671_j_mcma-2024-2015_ref_002","doi-asserted-by":"crossref","unstructured":"N. Aries and N. Mamode Khan,\nOn periodic integer-valued moving average (INMA (\ud835\udc5e)) models,\nJ. Stat. Comput. Simul. 93 (2023), no. 3, 366\u2013396.","DOI":"10.1080\/00949655.2022.2108031"},{"key":"2024112721095514671_j_mcma-2024-2015_ref_003","doi-asserted-by":"crossref","unstructured":"M. Bentarzi and N. Aries,\nOn some periodic \n                  \n                     \n                        \n                           I\n                           \u2062\n                           N\n                           \u2062\n                           A\n                           \u2062\n                           R\n                           \u2062\n                           M\n                           \u2062\n                           A\n                        \n                     \n                     \n                     INARMA\n                  \n               (\ud835\udc5d,\ud835\udc5e) models,\nComm. Statist. Simulation Comput. 51 (2022), no. 10, 5773\u20135793.","DOI":"10.1080\/03610918.2020.1780443"},{"key":"2024112721095514671_j_mcma-2024-2015_ref_004","doi-asserted-by":"crossref","unstructured":"M. Bourguignon, J. Rodrigues and M. Santos-Neto,\nExtended Poisson INAR(1) processes with equidispersion, underdispersion and overdispersion,\nJ. Appl. Stat. 46 (2019), no. 1, 101\u2013118.","DOI":"10.1080\/02664763.2018.1458216"},{"key":"2024112721095514671_j_mcma-2024-2015_ref_005","doi-asserted-by":"crossref","unstructured":"E. T. da Cunha, M. Bourguignon and K. L. P. Vasconcellos,\nOn shifted integer-valued autoregressive model for count time series showing equidispersion, underdispersion or overdispersion,\nComm. Statist. Theory Methods 50 (2021), no. 20, 4822\u20134843.","DOI":"10.1080\/03610926.2020.1725822"},{"key":"2024112721095514671_j_mcma-2024-2015_ref_006","unstructured":"J.-P. Dion, G. Gauthier and A. Latour,\nBranching processes with immigration and integer-valued time series,\nSerdica Math. J. 21 (1995), no. 2, 123\u2013136."},{"key":"2024112721095514671_j_mcma-2024-2015_ref_007","doi-asserted-by":"crossref","unstructured":"R. Ferland, A. Latour and D. Oraichi,\nInteger-valued GARCH process,\nJ. Time Ser. Anal. 27 (2006), no. 6, 923\u2013942.","DOI":"10.1111\/j.1467-9892.2006.00496.x"},{"key":"2024112721095514671_j_mcma-2024-2015_ref_008","doi-asserted-by":"crossref","unstructured":"K. Fokianos,\nCount time series models,\nHandbook of Statistics. Vol. 30,\nElsevier, Amsterdam (2012), 315\u2013347.","DOI":"10.1016\/B978-0-444-53858-1.00012-0"},{"key":"2024112721095514671_j_mcma-2024-2015_ref_009","unstructured":"J. Franke and T. Rao Subba,\nMultivariate first-order integer-valued autoregressions,\nTechnical Report, Technische Universit\u00e4t Kaiserslautern, 1995."},{"key":"2024112721095514671_j_mcma-2024-2015_ref_010","unstructured":"R. K. Freeland,\nStatistical analysis of discrete-time series with applications to the analysis of workers compensation claims data, PhD thesis,\nUniversity of British Columbia, Canada, 1998."},{"key":"2024112721095514671_j_mcma-2024-2015_ref_011","doi-asserted-by":"crossref","unstructured":"R. K. Freeland and B. McCabe,\nAsymptotic properties of CLS estimators in the Poisson \n                  \n                     \n                        \n                           AR\n                           \u2062\n                           \n                              (\n                              1\n                              )\n                           \n                        \n                     \n                     \n                     \\mathrm{AR}(1)\n                  \n                model,\nStatist. Probab. Lett. 73 (2005), no. 2, 147\u2013153.","DOI":"10.1016\/j.spl.2005.03.006"},{"key":"2024112721095514671_j_mcma-2024-2015_ref_012","unstructured":"E. G. Glady\u0161ev,\nPeriodically correlated random sequences,\nSoviet Math. 2 (1961), 385\u2013388."},{"key":"2024112721095514671_j_mcma-2024-2015_ref_013","doi-asserted-by":"crossref","unstructured":"J. Huang and F. 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Anal. 27 (2006), no. 5, 725\u2013738.","DOI":"10.1111\/j.1467-9892.2006.00485.x"}],"container-title":["Monte Carlo Methods and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/mcma-2024-2015\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/mcma-2024-2015\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,11,27]],"date-time":"2024-11-27T21:10:36Z","timestamp":1732741836000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/mcma-2024-2015\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,9,26]]},"references-count":29,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2024,11,14]]},"published-print":{"date-parts":[[2024,12,1]]}},"alternative-id":["10.1515\/mcma-2024-2015"],"URL":"https:\/\/doi.org\/10.1515\/mcma-2024-2015","relation":{},"ISSN":["0929-9629","1569-3961"],"issn-type":[{"type":"print","value":"0929-9629"},{"type":"electronic","value":"1569-3961"}],"subject":[],"published":{"date-parts":[[2024,9,26]]}}}