{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,3]],"date-time":"2026-06-03T14:34:48Z","timestamp":1780497288498,"version":"3.54.1"},"reference-count":54,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2023,1,21]],"date-time":"2023-01-21T00:00:00Z","timestamp":1674259200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>This manuscript deals with a parameter estimation of a non-negative integer-valued (NNIV) time series based on the so-called probability generating function (PGF) method. The theoretical background of the PGF estimation technique for a very general, stationary class of NNIV time series is described, as well as the asymptotic properties of the obtained estimates. After that, a particular emphasis is given to PGF estimators of independent identical distributed (IID) and integer-valued non-negative autoregressive (INAR) series. A Monte Carlo study of the thus obtained PGF estimates, based on a numerical integration of the appropriate objective function, is also presented. For this purpose, numerical quadrature formulas were computed using Gegenbauer orthogonal polynomials. Finally, the application of the PGF estimators in the dynamic analysis of some actual data is given.<\/jats:p>","DOI":"10.3390\/axioms12020112","type":"journal-article","created":{"date-parts":[[2023,1,23]],"date-time":"2023-01-23T01:36:26Z","timestamp":1674437786000},"page":"112","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Parameters Estimation in Non-Negative Integer-Valued Time Series: Approach Based on Probability Generating Functions"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3819-4387","authenticated-orcid":false,"given":"Vladica","family":"Stojanovi\u0107","sequence":"first","affiliation":[{"name":"Department of Informatics & Computer Sciences, University of Criminal Investigation and Police Studies, 11000 Belgrade, Serbia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8546-571X","authenticated-orcid":false,"given":"Eugen","family":"Ljajko","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Sciences & Mathematics, University of Pri\u0161tina in Kosovska Mitrovica, 38220 Kosovska Mitrovica, Serbia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4001-6907","authenticated-orcid":false,"given":"Marina","family":"To\u0161i\u0107","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Sciences & Mathematics, University of Pri\u0161tina in Kosovska Mitrovica, 38220 Kosovska Mitrovica, Serbia"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,1,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Johnson, N.L., Kemp, A.W., and Kotz, S. 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