Parameters Estimation in Non-Negative Integer-Valued Time Series: Approach Based on Probability Generating Functions
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,...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-01-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/12/2/112 |
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| author | Vladica Stojanović Eugen Ljajko Marina Tošić |
| author_facet | Vladica Stojanović Eugen Ljajko Marina Tošić |
| author_sort | Vladica Stojanović |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-11T09:10:33Z |
| format | Article |
| id | doaj.art-ee35d7ec7cd44f48811b595ba76f287b |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-11T09:10:33Z |
| publishDate | 2023-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-ee35d7ec7cd44f48811b595ba76f287b2023-11-16T19:05:25ZengMDPI AGAxioms2075-16802023-01-0112211210.3390/axioms12020112Parameters Estimation in Non-Negative Integer-Valued Time Series: Approach Based on Probability Generating FunctionsVladica Stojanović0Eugen Ljajko1Marina Tošić2Department of Informatics & Computer Sciences, University of Criminal Investigation and Police Studies, 11000 Belgrade, SerbiaDepartment of Mathematics, Faculty of Sciences & Mathematics, University of Priština in Kosovska Mitrovica, 38220 Kosovska Mitrovica, SerbiaDepartment of Mathematics, Faculty of Sciences & Mathematics, University of Priština in Kosovska Mitrovica, 38220 Kosovska Mitrovica, SerbiaThis 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.https://www.mdpi.com/2075-1680/12/2/112integer-valued time seriesparameter estimationprobability generating functionsasymptotic propertiessimulationnumerical integration |
| spellingShingle | Vladica Stojanović Eugen Ljajko Marina Tošić Parameters Estimation in Non-Negative Integer-Valued Time Series: Approach Based on Probability Generating Functions Axioms integer-valued time series parameter estimation probability generating functions asymptotic properties simulation numerical integration |
| title | Parameters Estimation in Non-Negative Integer-Valued Time Series: Approach Based on Probability Generating Functions |
| title_full | Parameters Estimation in Non-Negative Integer-Valued Time Series: Approach Based on Probability Generating Functions |
| title_fullStr | Parameters Estimation in Non-Negative Integer-Valued Time Series: Approach Based on Probability Generating Functions |
| title_full_unstemmed | Parameters Estimation in Non-Negative Integer-Valued Time Series: Approach Based on Probability Generating Functions |
| title_short | Parameters Estimation in Non-Negative Integer-Valued Time Series: Approach Based on Probability Generating Functions |
| title_sort | parameters estimation in non negative integer valued time series approach based on probability generating functions |
| topic | integer-valued time series parameter estimation probability generating functions asymptotic properties simulation numerical integration |
| url | https://www.mdpi.com/2075-1680/12/2/112 |
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