{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,13]],"date-time":"2026-02-13T19:35:58Z","timestamp":1771011358521,"version":"3.50.1"},"reference-count":44,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2020,11,16]],"date-time":"2020-11-16T00:00:00Z","timestamp":1605484800000},"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":"publisher","award":["2018R1A2A2A05019433"],"award-info":[{"award-number":["2018R1A2A2A05019433"]}],"id":[{"id":"10.13039\/501100003725","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In this study, we consider an online monitoring procedure to detect a parameter change for integer-valued generalized autoregressive heteroscedastic (INGARCH) models whose conditional density of present observations over past information follows one parameter exponential family distributions. For this purpose, we use the cumulative sum (CUSUM) of score functions deduced from the objective functions, constructed for the minimum power divergence estimator (MDPDE) that includes the maximum likelihood estimator (MLE), to diminish the influence of outliers. It is well-known that compared to the MLE, the MDPDE is robust against outliers with little loss of efficiency. This robustness property is properly inherited by the proposed monitoring procedure. A simulation study and real data analysis are conducted to affirm the validity of our method.<\/jats:p>","DOI":"10.3390\/e22111304","type":"journal-article","created":{"date-parts":[[2020,11,16]],"date-time":"2020-11-16T11:04:20Z","timestamp":1605524660000},"page":"1304","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Monitoring Parameter Change for Time Series Models of Counts Based on Minimum Density Power Divergence Estimator"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1109-6768","authenticated-orcid":false,"given":"Sangyeol","family":"Lee","sequence":"first","affiliation":[{"name":"Department of Statistics, Seoul National University, Seoul 08826, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dongwon","family":"Kim","sequence":"additional","affiliation":[{"name":"Department of Statistics, Seoul National University, Seoul 08826, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,11,16]]},"reference":[{"key":"ref_1","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":"J. Am. Water Resour. Assoc."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"261","DOI":"10.1111\/j.1467-9892.1987.tb00438.x","article-title":"First order integer-valued autoregressive (INAR(1)) process","volume":"8","author":"Alzaid","year":"1987","journal-title":"J. Time Ser. Anal."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"923","DOI":"10.1111\/j.1467-9892.2006.00496.x","article-title":"Integer-valued GARCH processes","volume":"27","author":"Ferland","year":"2006","journal-title":"J. Time Ser. Anal."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1430","DOI":"10.1198\/jasa.2009.tm08270","article-title":"Poisson autoregression","volume":"104","author":"Fokianos","year":"2009","journal-title":"J. Am. Stat. Assoc."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Wei\u00df, C.H. (2018). An Introduction to Discrete-Valued Time Series, Wiley.","DOI":"10.1002\/9781119097013"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"735","DOI":"10.1093\/biomet\/asp029","article-title":"A negative binomial model for time series of counts","volume":"96","author":"Davis","year":"2009","journal-title":"Biometrika"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"58","DOI":"10.1016\/j.jmaa.2011.11.042","article-title":"Modeling overdispersed or underdispersed count data with generalized poisson integer-valued garch models","volume":"389","author":"Zhu","year":"2012","journal-title":"J. Math. Anal. Appl."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"826","DOI":"10.1016\/j.jspi.2011.10.002","article-title":"Zero-inflated Poisson and negative binomial integer-valued GARCH models","volume":"142","author":"Zhu","year":"2012","journal-title":"J. Stat. Plan. Infer."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"954","DOI":"10.1111\/j.1467-9892.2012.00809.x","article-title":"First-order integer valued AR processes with zero inflated poisson innovations","volume":"33","author":"Jazi","year":"2012","journal-title":"J. Time Ser. Anal."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1111\/jtsa.12050","article-title":"Quasi-likelihood inference for negative binomial time series models","volume":"35","author":"Christou","year":"2014","journal-title":"J. Time Ser. Anal."},{"key":"ref_11","first-page":"1673","article-title":"Theory and inference for a class of observation-driven models with application to time series of counts","volume":"26","author":"Davis","year":"2016","journal-title":"Stat. Sin."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"540","DOI":"10.1080\/02331888.2015.1083020","article-title":"Parameter change test for zero-inflated generalized Poisson autoregressive models","volume":"50","author":"Lee","year":"2016","journal-title":"Statistics"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"963","DOI":"10.1111\/rssc.12344","article-title":"Markov switching integer-valued generalized autoregressive conditional heteroscedastic models for dengue counts","volume":"68","author":"Chen","year":"2019","journal-title":"J. Roy. Stat. Soc. C"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"523","DOI":"10.1093\/biomet\/42.3-4.523","article-title":"A test for a change in a parameter occurring at an unknown point","volume":"42","author":"Page","year":"1955","journal-title":"Biometrika"},{"key":"ref_15","unstructured":"Cs\u00f6rgo, M., and Horv\u00e1th, L. (1997). Limit Theorems in Change-Point Analysis., John Wiley & Sons Inc."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Chen, J., and Gupta, A.K. (2012). Parametric Statistical Change Point Analysis with Applications to Genetics, Medicine, and Finance, Wiley.","DOI":"10.1007\/978-0-8176-4801-5"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"781","DOI":"10.1111\/1467-9469.00364","article-title":"The CUSUM test for parameter change in time series models","volume":"30","author":"Lee","year":"2003","journal-title":"Scand. J. Stat."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"210","DOI":"10.1111\/j.1467-9892.2010.00657.x","article-title":"Interventions in INGARCH processes","volume":"31","author":"Fokianos","year":"2010","journal-title":"J. Time Ser. Anal."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"299","DOI":"10.1177\/1471082X1201200401","article-title":"Interventions in log-linear Poisson autoregression","volume":"12","author":"Fokianos","year":"2012","journal-title":"Stat. Model."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"757","DOI":"10.1111\/j.1467-9892.2011.00778.x","article-title":"Changepoints in times series of counts","volume":"33","author":"Franke","year":"2012","journal-title":"J. Time Ser. Anal."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"102","DOI":"10.1016\/j.jspi.2013.08.017","article-title":"Retrospective change detection for binary time series models","volume":"145","author":"Fokianos","year":"2014","journal-title":"J. Stat. Plan. Infer."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1744","DOI":"10.1016\/j.jspi.2013.05.009","article-title":"Structural changes in autoregressive models for binary time series","volume":"143","year":"2013","journal-title":"J. Stat. Plan. Infer."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"843","DOI":"10.1111\/sjos.12278","article-title":"Tests for structural changes in time series of counts","volume":"44","author":"Meintanis","year":"2017","journal-title":"Scand. J. Stat."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1136","DOI":"10.1111\/sjos.12088","article-title":"Parameter change test for Poisson autoregressive models","volume":"41","author":"Kang","year":"2014","journal-title":"Scand. J. Stat."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"52","DOI":"10.1007\/s11749-016-0510-6","article-title":"Asymptotic normality and parameter change test for bivariate Poisson INGARCH models","volume":"27","author":"Lee","year":"2018","journal-title":"Test"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1033","DOI":"10.1007\/s10463-018-0676-7","article-title":"CUSUM tests for general nonlinear inter-valued GARCH models: comparison study","volume":"71","author":"Lee","year":"2019","journal-title":"Ann. Inst. Stat. Math."},{"key":"ref_27","first-page":"111","article-title":"SPC method for time-dependent processes of counts - a literature review","volume":"2","year":"2015","journal-title":"Cogent Math."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"465","DOI":"10.1002\/qre.1764","article-title":"CUSUM control charts for the monitoring of zero-inflated binomial processes","volume":"32","author":"Rakitzis","year":"2016","journal-title":"Qual. Rel. Eng. Int."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"2371","DOI":"10.1002\/qre.2519","article-title":"Improved CUSUM monitoring of Markov counting process with frequent zeros","volume":"35","author":"Kim","year":"2019","journal-title":"Qual. Rel. Eng. Int."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"715","DOI":"10.1016\/j.jmva.2008.08.005","article-title":"Monitoring parameter change in AR(p) time series models","volume":"100","author":"Gombay","year":"2009","journal-title":"J. Multi. Anal."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1754","DOI":"10.1080\/00949655.2017.1284848","article-title":"Monitoring parameter shift with Poisson integer-valued GARCH models","volume":"87","author":"Huh","year":"2017","journal-title":"J. Stat. Comp. Sim."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"389","DOI":"10.1080\/00224065.2009.11917793","article-title":"CUSUM monitoring of first-order integer-valued autoregressive processes of Poisson counts","volume":"41","author":"Testik","year":"2009","journal-title":"J. Qual. Tech."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"549","DOI":"10.1093\/biomet\/85.3.549","article-title":"Robust and efficient estimation by minimizing a density power divergence","volume":"85","author":"Basu","year":"1998","journal-title":"Biometrika"},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Riani, M., Atkinson, A.C., Corbellini, A., and Perrotta, D. (2020). Robust Regression with Density Power Divergence: Theory, Comparisons, and Data Analysis. Entroby, 22.","DOI":"10.3390\/e22040399"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"2981","DOI":"10.1080\/00949655.2017.1351563","article-title":"Robust estimation for zero-inflated Poisson autoregressive models based on density power divergence","volume":"87","author":"Kim","year":"2017","journal-title":"J. Stat. Comput. Simul."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"1371","DOI":"10.1007\/s10463-019-00728-0","article-title":"Robust estimation for general integer-valued time series models","volume":"72","author":"Kim","year":"2020","journal-title":"Ann. Inst. Stat. Math."},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Kim, B., and Lee, S. (2020). Robust change point test for general integer-valued time series models based on density power divergence. Entropy, 22.","DOI":"10.3390\/e22040493"},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Kang, J., and Song, J. (2020). A robust approach for testing parameter change in Poisson autoregressive models. J. Korean Stat. Soc., in press.","DOI":"10.1007\/s42952-020-00056-7"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"571","DOI":"10.1016\/j.csda.2004.03.006","article-title":"A data-based method for selecting tuning parameters in minimum distance estimators","volume":"48","author":"Warwick","year":"2005","journal-title":"Comput. Stat. Data Anal."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"581","DOI":"10.1080\/00949650412331299120","article-title":"Choosing a robustness tuning parameter","volume":"75","author":"Warwick","year":"2005","journal-title":"J. Stat. Comput. Simul."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"793","DOI":"10.1214\/13-EJS790","article-title":"A goodness of fit test for Poisson count processes","volume":"7","author":"Fokianos","year":"2013","journal-title":"Electron. J. Stat."},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Billingsley, P. (1999). Convergence of Probability Measures, Wiley. [2nd ed.].","DOI":"10.1002\/9780470316962"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"567","DOI":"10.1017\/S0266466612000655","article-title":"A warp-speed method for conducting Monte Carlo experiments involving bootstrap estimators","volume":"29","author":"Giacomini","year":"2013","journal-title":"Econ. Theory"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1007\/s10260-011-0162-3","article-title":"Monitoring parameter change in time series models","volume":"20","author":"Na","year":"2011","journal-title":"Stat. Meth. Appl."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/22\/11\/1304\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T10:34:12Z","timestamp":1760178852000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/22\/11\/1304"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,11,16]]},"references-count":44,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2020,11]]}},"alternative-id":["e22111304"],"URL":"https:\/\/doi.org\/10.3390\/e22111304","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,11,16]]}}}