Parameters Estimation in Non-Negative Integer-Valued Time Series: Approach Based on Probability Generating Functions
Abstract
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.
Keywords:
integer-valued time series / parameter estimation / probability generating functions / asymptotic properties / simulation / numerical integration / applicationSource:
Axioms, 2023, 12, 2, 112-Publisher:
- Basel : MDPI
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Institution/Community
JakovTY - JOUR AU - Stojanović, Vladica AU - Ljajko, Eugen AU - Tošić, Marina PY - 2023 UR - https://jakov.kpu.edu.rs/handle/123456789/1645 AB - 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. PB - Basel : MDPI T2 - Axioms T1 - Parameters Estimation in Non-Negative Integer-Valued Time Series: Approach Based on Probability Generating Functions VL - 12 IS - 2 SP - 112 DO - 10.3390/axioms12020112 ER -
@article{ author = "Stojanović, Vladica and Ljajko, Eugen and Tošić, Marina", year = "2023", abstract = "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.", publisher = "Basel : MDPI", journal = "Axioms", title = "Parameters Estimation in Non-Negative Integer-Valued Time Series: Approach Based on Probability Generating Functions", volume = "12", number = "2", pages = "112", doi = "10.3390/axioms12020112" }
Stojanović, V., Ljajko, E.,& Tošić, M.. (2023). Parameters Estimation in Non-Negative Integer-Valued Time Series: Approach Based on Probability Generating Functions. in Axioms Basel : MDPI., 12(2), 112. https://doi.org/10.3390/axioms12020112
Stojanović V, Ljajko E, Tošić M. Parameters Estimation in Non-Negative Integer-Valued Time Series: Approach Based on Probability Generating Functions. in Axioms. 2023;12(2):112. doi:10.3390/axioms12020112 .
Stojanović, Vladica, Ljajko, Eugen, Tošić, Marina, "Parameters Estimation in Non-Negative Integer-Valued Time Series: Approach Based on Probability Generating Functions" in Axioms, 12, no. 2 (2023):112, https://doi.org/10.3390/axioms12020112 . .