{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:45:12Z","timestamp":1760143512630,"version":"build-2065373602"},"reference-count":28,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2024,2,15]],"date-time":"2024-02-15T00:00:00Z","timestamp":1707955200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The novel circumstance-driven bivariate integer-valued autoregressive (CuBINAR) model for non-stationary count time series is proposed. The non-stationarity of the bivariate count process is defined by a joint categorical sequence, which expresses the current state of the process. Additional cross-dependence can be generated via cross-dependent innovations. The model can also be equipped with a marginal bivariate Poisson distribution to make it suitable for low-count time series. Important stochastic properties of the new model are derived. The Yule\u2013Walker and conditional maximum likelihood method are adopted to estimate the unknown parameters. The consistency of these estimators is established, and their finite-sample performance is investigated by a simulation study. The scope and application of the model are illustrated by a real-world data example on sales counts, where a soap product in different stores with a common circumstance factor is investigated.<\/jats:p>","DOI":"10.3390\/e26020168","type":"journal-article","created":{"date-parts":[[2024,2,15]],"date-time":"2024-02-15T05:55:59Z","timestamp":1707976559000},"page":"168","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["The Circumstance-Driven Bivariate Integer-Valued Autoregressive Model"],"prefix":"10.3390","volume":"26","author":[{"given":"Huiqiao","family":"Wang","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, Helmut Schmidt University, Holstenhofweg 85, 22043 Hamburg, Germany"},{"name":"Department of Statistics, Southwestern University of Finance and Economics, Chengdu 611130, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8739-6631","authenticated-orcid":false,"given":"Christian H.","family":"Wei\u00df","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, Helmut Schmidt University, Holstenhofweg 85, 22043 Hamburg, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,2,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Wei\u00df, C. (2018). An Introduction to Discrete-Valued Time Series, Wiley.","DOI":"10.1002\/9781119097013"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"645","DOI":"10.1111\/j.1752-1688.1985.tb05379.x","article-title":"Some simple models for discrete variate time series","volume":"21","author":"McKenzie","year":"1985","journal-title":"JAWRA J. Am. Water Resour. Assoc."},{"key":"ref_3","first-page":"314","article-title":"First-order integer-valued autoregressive (INAR(1)) process","volume":"8","author":"Alzaid","year":"1987","journal-title":"J. Time Ser. Anal."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1007\/s10182-008-0072-3","article-title":"Thinning operations for modeling time series of counts\u2014A survey","volume":"92","year":"2008","journal-title":"AStA Adv. Stat. Anal."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"395","DOI":"10.1002\/(SICI)1099-095X(199907\/08)10:4<395::AID-ENV364>3.0.CO;2-M","article-title":"Integer-valued autoregressive models for tipping bucket rainfall measurements","volume":"10","author":"Thyregod","year":"1999","journal-title":"Environmetrics"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"2717","DOI":"10.1080\/03610926.2011.556292","article-title":"Integer-valued self-exciting threshold autoregressive processes","volume":"41","author":"Monteiro","year":"2012","journal-title":"Commun. Stat.-Theory Methods"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Steland, A., Rafaj\u0142owicz, E., and Szajowski, K. (2015). Stochastic Models, Statistics and Their Applications, Springer.","DOI":"10.1007\/978-3-319-13881-7"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"485","DOI":"10.1007\/s00362-006-0028-1","article-title":"A non-stationary integer-valued autoregressive model","volume":"49","author":"Kim","year":"2008","journal-title":"Stat. Pap."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1111\/jtsa.12161","article-title":"Random environment integer-valued autoregressive process","volume":"37","author":"Laketa","year":"2016","journal-title":"J. Time Ser. Anal."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1007\/s00009-017-1054-z","article-title":"Generalized random environment INAR models of higher order","volume":"15","author":"Laketa","year":"2016","journal-title":"Mediterr. J. Math."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1177\/1471082X1001100403","article-title":"A bivariate INAR(1) process with application","volume":"11","author":"Pedeli","year":"2011","journal-title":"Stat. Model."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"228","DOI":"10.2307\/1427868","article-title":"The multivariate GINAR(p) process","volume":"29","author":"Latour","year":"1997","journal-title":"Adv. Appl. Probab."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1016\/j.csda.2013.05.019","article-title":"Some properties of multivariate INAR(1) processes","volume":"67","author":"Pedeli","year":"2013","journal-title":"Comput. Stat. Data Anal."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"723","DOI":"10.1080\/03610926.2012.754466","article-title":"Flexible Bivariate INAR(1) Processes Using Copulas","volume":"42","author":"Karlis","year":"2013","journal-title":"Commun. Stat.-Theory Methods"},{"key":"ref_15","first-page":"1291","article-title":"On the theory of periodic multivariate INAR processes","volume":"69","author":"Santos","year":"2019","journal-title":"Stat. Pap."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"3106","DOI":"10.1080\/00949655.2016.1150482","article-title":"Modelling a non-stationary BINAR(1) Poisson process","volume":"86","author":"Khan","year":"2016","journal-title":"J. Stat. Comput. Simul."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1631","DOI":"10.1080\/03610918.2018.1502780","article-title":"BINMA(1) model with COM-Poisson innovations: Estimation and application","volume":"49","author":"Sunecher","year":"2018","journal-title":"Commun. Stat.-Simul. Comput."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"2546","DOI":"10.1080\/02664763.2020.1747411","article-title":"Inference for bivariate integer-valued moving average models based on binomial thinning operation","volume":"47","author":"Silva","year":"2020","journal-title":"J. Appl. Stat."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1016\/j.jmva.2013.12.014","article-title":"Bivariate binomial autoregressive models","volume":"125","author":"Scotto","year":"2014","journal-title":"J. Multivariate Anal."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1016\/j.jspi.2019.05.004","article-title":"Bivariate first-order random coefficient integer-valued autoregressive processes","volume":"204","author":"Yu","year":"2020","journal-title":"J. Stat. Plan. Inference"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"428","DOI":"10.1007\/s11749-017-0552-4","article-title":"A new bivariate integer-valued GARCH model allowing for negative cross-correlation","volume":"27","author":"Cui","year":"2018","journal-title":"Test"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"788","DOI":"10.1111\/jtsa.12459","article-title":"Flexible and robust mixed Poisson INGARCH models","volume":"40","author":"Silva","year":"2019","journal-title":"J. Time Ser. Anal."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"206","DOI":"10.1111\/jtsa.12663","article-title":"Flexible bivariate INGARCH process with a broad range of contemporaneous correlation","volume":"44","author":"Piancastelli","year":"2023","journal-title":"J. Time Ser. Anal."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"408","DOI":"10.1214\/17-AOAS1098","article-title":"Multivariate integer-valued time series with flexible autocovariances and their application to major hurricane counts","volume":"12","author":"Livsey","year":"2018","journal-title":"Ann. Appl. Stat."},{"key":"ref_25","first-page":"355","article-title":"Forecasting with two generalized integer-valued autoregressive processes of order one in the mutual random environment","volume":"43","author":"Laketa","year":"2019","journal-title":"SORT-Stat. Oper. Res. Trans."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Davis, R.A., Holan, S.H., Lund, R., and Ravishanker, N. (2016). Handbook of Discrete-Valued Time Series, CRC Press.","DOI":"10.1201\/b19485"},{"key":"ref_27","unstructured":"Contreras-Reyes, J.E. Information quantity evaluation of multivariate SETAR processes of order one and applications, Stat. Pap., in press."},{"key":"ref_28","unstructured":"White, H. (2001). Asymptotic Theory For Econometricians, Academic Press."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/26\/2\/168\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T14:00:02Z","timestamp":1760104802000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/26\/2\/168"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,2,15]]},"references-count":28,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2024,2]]}},"alternative-id":["e26020168"],"URL":"https:\/\/doi.org\/10.3390\/e26020168","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2024,2,15]]}}}