{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,14]],"date-time":"2026-03-14T22:05:04Z","timestamp":1773525904345,"version":"3.50.1"},"reference-count":30,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2020,3,27]],"date-time":"2020-03-27T00:00:00Z","timestamp":1585267200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2020,3,27]],"date-time":"2020-03-27T00:00:00Z","timestamp":1585267200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100003725","name":"National Research Foundation of Korea","doi-asserted-by":"crossref","award":["NRF-2018R1D1A1B07045707"],"award-info":[{"award-number":["NRF-2018R1D1A1B07045707"]}],"id":[{"id":"10.13039\/501100003725","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comput Stat"],"published-print":{"date-parts":[[2020,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We focus on purely autoregressive (AR)-type models defined on the bounded range <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\{0,1,\\ldots , n\\}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mo>{<\/mml:mo>\n                    <mml:mn>0<\/mml:mn>\n                    <mml:mo>,<\/mml:mo>\n                    <mml:mn>1<\/mml:mn>\n                    <mml:mo>,<\/mml:mo>\n                    <mml:mo>\u2026<\/mml:mo>\n                    <mml:mo>,<\/mml:mo>\n                    <mml:mi>n<\/mml:mi>\n                    <mml:mo>}<\/mml:mo>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> with a fixed upper limit <jats:inline-formula><jats:alternatives><jats:tex-math>$$n \\in \\mathbb {N}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>n<\/mml:mi>\n                    <mml:mo>\u2208<\/mml:mo>\n                    <mml:mi>N<\/mml:mi>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>. These include the binomial AR model, binomial AR conditional heteroscedasticity (ARCH) model, binomial-variation AR model with their linear conditional mean, nonlinear max-binomial AR model, and binomial logit-ARCH model. We consider the key problem of identifying which of these AR-type models is the true data-generating process. Despite the volume of the literature on model selection, little is known about this procedure in the context of nonnested and nonlinear time series models for counts. We consider the most popular approaches used for model identification, Akaike\u2019s information criterion and the Bayesian information criterion, and compare them using extensive Monte Carlo simulations. Furthermore, we investigate the properties of the fitted models (both the correct and wrong models) obtained using maximum likelihood estimation. A real-data example demonstrates our findings.<\/jats:p>","DOI":"10.1007\/s00180-020-00980-6","type":"journal-article","created":{"date-parts":[[2020,3,27]],"date-time":"2020-03-27T06:02:57Z","timestamp":1585288977000},"page":"1715-1736","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Models for autoregressive processes of bounded counts: How different are they?"],"prefix":"10.1007","volume":"35","author":[{"given":"Hee-Young","family":"Kim","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8739-6631","authenticated-orcid":false,"given":"Christian H.","family":"Wei\u00df","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6581-0376","authenticated-orcid":false,"given":"Tobias A.","family":"M\u00f6ller","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,3,27]]},"reference":[{"issue":"6","key":"980_CR1","first-page":"717","volume":"19","author":"H Akaike","year":"1974","unstructured":"Akaike H (1974) A new look at the statistical model identification. IEEE Trans Autom Control 19(6):717\u2013723","journal-title":"IEEE Trans Autom Control"},{"issue":"3","key":"980_CR2","doi-asserted-by":"publisher","first-page":"261","DOI":"10.1111\/j.1467-9892.1987.tb00438.x","volume":"8","author":"MA Al-Osh","year":"1987","unstructured":"Al-Osh MA, Alzaid AA (1987) First-order integer-valued autoregressive (INAR(1)) process. J Time Ser Anal 8(3):261\u2013275","journal-title":"J Time Ser Anal"},{"key":"980_CR3","volume-title":"Model selection and multimodel inference: a practical information-theoretic approach","author":"KP Burnham","year":"2002","unstructured":"Burnham KP, Anderson DR (2002) Model selection and multimodel inference: a practical information-theoretic approach, 2nd edn. Springer, New York","edition":"2"},{"issue":"3","key":"980_CR4","doi-asserted-by":"publisher","first-page":"e1460","DOI":"10.1002\/wics.1460","volume":"11","author":"JE Cavanaugh","year":"2019","unstructured":"Cavanaugh JE, Neath AA (2019) The Akaike information criterion: background, derivation, properties, application, interpretation, and refinements. WIREs Comput Stat 11(3):e1460","journal-title":"WIREs Comput Stat"},{"key":"980_CR5","doi-asserted-by":"crossref","unstructured":"Chen H, Li Q, Zhu F (2019) Two classes of dynamic binomial integer-valued ARCH models. Braz J Probab Stat, forthcoming","DOI":"10.1214\/19-BJPS452"},{"key":"980_CR6","volume-title":"Model selection and model averaging","author":"G Claeskens","year":"2008","unstructured":"Claeskens G, Hjort NL (2008) Model selection and model averaging. Cambridge University Press, Cambridge"},{"issue":"4","key":"980_CR7","doi-asserted-by":"publisher","first-page":"781","DOI":"10.1093\/biomet\/asp057","volume":"96","author":"Y Cui","year":"2009","unstructured":"Cui Y, Lund R (2009) A new look at time series of counts. Biometrika 96(4):781\u2013792","journal-title":"Biometrika"},{"issue":"4","key":"980_CR8","doi-asserted-by":"publisher","first-page":"781","DOI":"10.2307\/1427767","volume":"21","author":"RA Davis","year":"1989","unstructured":"Davis RA, Resnick SI (1989) Basic properties and prediction of max-ARMA processes. Adv Appl Prob 21(4):781\u2013803","journal-title":"Adv Appl Prob"},{"key":"980_CR9","unstructured":"Diop ML, Kenge W (2020) Consistent model selection procedure for general integer-valued time series. arXiv:2002.08789"},{"key":"980_CR10","unstructured":"Dziak JJ, Coffman DL, Lanza ST, Li R, Jermiin LS (2019) Sensitivity and specificity of information criteria. Brief Bioinform, bbz016"},{"issue":"9","key":"980_CR11","doi-asserted-by":"publisher","first-page":"2495","DOI":"10.1007\/s00477-018-1584-3","volume":"32","author":"S Gouveia","year":"2018","unstructured":"Gouveia S, M\u00f6ller TA, Wei\u00df CH, Scotto MG (2018) A full ARMA model for counts with bounded support and its application to rainy-days time series. Stoch Environ Res Risk Assess 32(9):2495\u20132514","journal-title":"Stoch Environ Res Risk Assess"},{"issue":"4","key":"980_CR12","doi-asserted-by":"publisher","first-page":"479","DOI":"10.1111\/1467-842X.00143","volume":"42","author":"G Grunwald","year":"2000","unstructured":"Grunwald G, Hyndman RJ, Tedesco L, Tweedie RL (2000) Non-Gaussian conditional linear AR(1) models. Aust N Z J Stat 42(4):479\u2013495","journal-title":"Aust N Z J Stat"},{"key":"980_CR13","first-page":"189","volume-title":"Handbook of discrete-valued time series","author":"RC Jung","year":"2016","unstructured":"Jung RC, McCabe BPM, Tremayne AR (2016) Model validation and diagnostics. In: Davis RA et al (eds) Handbook of discrete-valued time series. CRC Press, Boca Raton, pp 189\u2013218"},{"issue":"3","key":"980_CR14","doi-asserted-by":"publisher","first-page":"243","DOI":"10.2307\/1267787","volume":"23","author":"RW Katz","year":"1981","unstructured":"Katz RW (1981) On some criteria for estimating the order of a Markov chain. Technometrics 23(3):243\u2013249","journal-title":"Technometrics"},{"issue":"1","key":"980_CR15","doi-asserted-by":"publisher","first-page":"61","DOI":"10.1111\/j.1467-9892.2011.00740.x","volume":"33","author":"T Kunihama","year":"2012","unstructured":"Kunihama T, Omori Y, Zhang Z (2012) Efficient estimation and particle filter for max-stable processes. J Time Ser Anal 33(1):61\u201380","journal-title":"J Time Ser Anal"},{"issue":"4","key":"980_CR16","doi-asserted-by":"publisher","first-page":"645","DOI":"10.1111\/j.1752-1688.1985.tb05379.x","volume":"21","author":"E McKenzie","year":"1985","unstructured":"McKenzie E (1985) Some simple models for discrete variate time series. Water Res Bull 21(4):645\u2013650","journal-title":"Water Res Bull"},{"issue":"2","key":"980_CR17","doi-asserted-by":"publisher","first-page":"199","DOI":"10.1002\/wics.199","volume":"4","author":"AA Neath","year":"2012","unstructured":"Neath AA, Cavanaugh JE (2012) The Bayesian information criterion: background, derivation, and applications. WIREs Comput Stat 4(2):199\u2013203","journal-title":"WIREs Comput Stat"},{"issue":"4","key":"980_CR18","doi-asserted-by":"publisher","first-page":"369","DOI":"10.1111\/j.1467-9892.2009.00614.x","volume":"30","author":"Z Psaradakis","year":"2009","unstructured":"Psaradakis Z, Sola M, Spagnoloy F (2009) Selecting nonlinear time series models using information criteria. J Time Ser Anal 30(4):369\u2013394","journal-title":"J Time Ser Anal"},{"issue":"3","key":"980_CR19","first-page":"325","volume":"20","author":"S Rinke","year":"2016","unstructured":"Rinke S, Sibbertsen P (2016) Information criteria for nonlinear time series models. Stud Nonlinear Dyn Econ 20(3):325\u2013341","journal-title":"Stud Nonlinear Dyn Econ"},{"issue":"2","key":"980_CR20","doi-asserted-by":"publisher","first-page":"20150051","DOI":"10.1515\/ijb-2015-0051","volume":"12","author":"MM Risti\u0107","year":"2016","unstructured":"Risti\u0107 MM, Wei\u00df CH, Janji\u0107 AD (2016) A binomial integer-valued ARCH model. Int J Biostat 12(2):20150051","journal-title":"Int J Biostat"},{"issue":"2","key":"980_CR21","doi-asserted-by":"publisher","first-page":"461","DOI":"10.1214\/aos\/1176344136","volume":"6","author":"G Schwarz","year":"1978","unstructured":"Schwarz G (1978) Estimating the dimension of a model. Ann Stat 6(2):461\u2013464","journal-title":"Ann Stat"},{"issue":"5","key":"980_CR22","doi-asserted-by":"publisher","first-page":"893","DOI":"10.1214\/aop\/1176994950","volume":"7","author":"FW Steutel","year":"1979","unstructured":"Steutel FW, van Harn K (1979) Discrete analogues of self-decomposability and stability. Ann Probab 7(5):893\u2013899","journal-title":"Ann Probab"},{"issue":"4","key":"980_CR23","doi-asserted-by":"publisher","first-page":"447","DOI":"10.1080\/03610920802233937","volume":"38","author":"CH Wei\u00df","year":"2009","unstructured":"Wei\u00df CH (2009) A new class of autoregressive models for time series of binomial counts. Commun Stat Theory Methods 38(4):447\u2013460","journal-title":"Commun Stat Theory Methods"},{"key":"980_CR24","doi-asserted-by":"publisher","DOI":"10.1002\/9781119097013","volume-title":"An introduction to discrete-valued time series","author":"CH Wei\u00df","year":"2018","unstructured":"Wei\u00df CH (2018) An introduction to discrete-valued time series. Wiley, Chichester"},{"issue":"1","key":"980_CR25","doi-asserted-by":"crossref","first-page":"20180012","DOI":"10.1515\/snde-2018-0012","volume":"24","author":"CH Wei\u00df","year":"2020","unstructured":"Wei\u00df CH, Feld MH-JM (2020) On the performance of information criteria for model identification of count time series. Stud Nonlinear Dyn Econom 24(1):20180012","journal-title":"Stud Nonlinear Dyn Econom"},{"issue":"2","key":"980_CR26","doi-asserted-by":"publisher","first-page":"284","DOI":"10.3390\/stats2020022","volume":"2","author":"CH Wei\u00df","year":"2019","unstructured":"Wei\u00df CH, Feld MH-JM, Mamode Khan N, Sunecher Y (2019) INARMA modeling of count time series. Stats 2(2):284\u2013320","journal-title":"Stats"},{"issue":"3","key":"980_CR27","doi-asserted-by":"publisher","first-page":"563","DOI":"10.1007\/s00362-012-0449-y","volume":"54","author":"CH Wei\u00df","year":"2013","unstructured":"Wei\u00df CH, Kim H-Y (2013) Parameter estimation for binomial AR(1) models with applications in finance and industry. Stat Pap 54(3):563\u2013590","journal-title":"Stat Pap"},{"issue":"3","key":"980_CR28","doi-asserted-by":"publisher","first-page":"815","DOI":"10.1111\/j.1541-0420.2011.01716.x","volume":"68","author":"CH Wei\u00df","year":"2012","unstructured":"Wei\u00df CH, Pollett PK (2012) Chain binomial models and binomial autoregressive processes. Biometrics 68(3):815\u2013824","journal-title":"Biometrics"},{"key":"980_CR29","doi-asserted-by":"publisher","first-page":"28","DOI":"10.1016\/j.spl.2018.07.011","volume":"143","author":"CH Wei\u00df","year":"2018","unstructured":"Wei\u00df CH, Scotto MG, M\u00f6ller TA, Gouveia S (2018) The max-BARMA models for counts with bounded support. Stat Probab Lett 143:28\u201336","journal-title":"Stat Probab Lett"},{"issue":"5","key":"980_CR30","doi-asserted-by":"publisher","first-page":"1135","DOI":"10.1016\/j.jspi.2009.10.014","volume":"140","author":"Z Zhang","year":"2010","unstructured":"Zhang Z, Smith RL (2010) On the estimation and application of max-stable processes. J Stat Plan Inference 140(5):1135\u20131153","journal-title":"J Stat Plan Inference"}],"container-title":["Computational Statistics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00180-020-00980-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00180-020-00980-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00180-020-00980-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,3,27]],"date-time":"2021-03-27T00:13:55Z","timestamp":1616804035000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00180-020-00980-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,3,27]]},"references-count":30,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2020,12]]}},"alternative-id":["980"],"URL":"https:\/\/doi.org\/10.1007\/s00180-020-00980-6","relation":{},"ISSN":["0943-4062","1613-9658"],"issn-type":[{"value":"0943-4062","type":"print"},{"value":"1613-9658","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,3,27]]},"assertion":[{"value":"25 September 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"11 March 2020","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 March 2020","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}