Axioms, 2023-01, Vol.12 (2), p.112
2023
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Details
- Autor(en) / Beteiligte
- Titel
- Parameters Estimation in Non-Negative Integer-Valued Time Series: Approach Based on Probability Generating Functions
- Ist Teil von
- Axioms, 2023-01, Vol.12 (2), p.112
- Ort / Verlag
- Basel: MDPI AG
- Erscheinungsjahr
- 2023
- Quelle
- EZB Electronic Journals Library
- Beschreibungen/Notizen
- 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.
- Sprache
- Englisch
- Identifikatoren
- ISSN: 2075-1680eISSN: 2075-1680DOI: 10.3390/axioms12020112Titel-ID: cdi_doaj_primary_oai_doaj_org_article_ee35d7ec7cd44f48811b595ba76f287b
- Format
- –
- Schlagworte
- Asymptotic properties, COVID-19, Estimates, Estimators, Generating functions, integer-valued time series, Integers, Mathematical functions, Mathematical research, Maximum likelihood method, Numerical integration, Parameter estimation, Polynomials, probability generating functions, Quadratures, Random variables, simulation, Stochastic models, Time series, Time-series analysis