{"title":"A bilinear modeling in counts time series with applications","authors":"","doi":"10.1016/j.cnsns.2024.108282","DOIUrl":null,"url":null,"abstract":"<div><p>This paper introduces a modified bilinear model for integer-valued time series in which thinning operators are applied in bilinear terms involving the product of the input and state process separately. The proposed model is able to consider overdispersion. Furthermore, it connects a feature of the integer-valued autoregressive conditional heteroskedasticity and integer-valued autoregressive processes. Important properties of the proposed model as well as the sufficient condition for stationarity are derived. After considering some estimation methods based on time domain and frequency domain approaches, simulation studies are conducted to check the performance of the estimates. The analysis of practical cases in social science is accomplished to highlight the usefulness of the proposed model in applications, and the model’s adequacy is provided. Further, the suggested model discusses the problem of data forecasting.</p></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":null,"pages":null},"PeriodicalIF":3.4000,"publicationDate":"2024-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications in Nonlinear Science and Numerical Simulation","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1007570424004672","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
This paper introduces a modified bilinear model for integer-valued time series in which thinning operators are applied in bilinear terms involving the product of the input and state process separately. The proposed model is able to consider overdispersion. Furthermore, it connects a feature of the integer-valued autoregressive conditional heteroskedasticity and integer-valued autoregressive processes. Important properties of the proposed model as well as the sufficient condition for stationarity are derived. After considering some estimation methods based on time domain and frequency domain approaches, simulation studies are conducted to check the performance of the estimates. The analysis of practical cases in social science is accomplished to highlight the usefulness of the proposed model in applications, and the model’s adequacy is provided. Further, the suggested model discusses the problem of data forecasting.
期刊介绍：
The journal publishes original research findings on experimental observation, mathematical modeling, theoretical analysis and numerical simulation, for more accurate description, better prediction or novel application, of nonlinear phenomena in science and engineering. It offers a venue for researchers to make rapid exchange of ideas and techniques in nonlinear science and complexity.
The submission of manuscripts with cross-disciplinary approaches in nonlinear science and complexity is particularly encouraged.
Topics of interest:
Nonlinear differential or delay equations, Lie group analysis and asymptotic methods, Discontinuous systems, Fractals, Fractional calculus and dynamics, Nonlinear effects in quantum mechanics, Nonlinear stochastic processes, Experimental nonlinear science, Time-series and signal analysis, Computational methods and simulations in nonlinear science and engineering, Control of dynamical systems, Synchronization, Lyapunov analysis, High-dimensional chaos and turbulence, Chaos in Hamiltonian systems, Integrable systems and solitons, Collective behavior in many-body systems, Biological physics and networks, Nonlinear mechanical systems, Complex systems and complexity.
No length limitation for contributions is set, but only concisely written manuscripts are published. Brief papers are published on the basis of Rapid Communications. Discussions of previously published papers are welcome.
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