Stability conditions of limit cycle for Gompertz Autoregressive model
Article Sidebar
Main Article Content
Abstract
In this paper, we suggest Gompertz Autoregressive model by using the cumulative distribution function of Gompertz distribution and, the aim of this paper is studying and finding the stability conditions of a limit cycle for the Gompertz Autoregressive model with period, with giving some examples for Gompertz AR (1) to explain the orbital stable or the orbital unstable with plots the trajectories with different initial values.
Article Details
This work is licensed under a Creative Commons Attribution 4.0 International License.
Tikrit Journal of Pure Science is licensed under the Creative Commons Attribution 4.0 International License, which allows users to copy, create extracts, abstracts, and new works from the article, alter and revise the article, and make commercial use of the article (including reuse and/or resale of the article by commercial entities), provided the user gives appropriate credit (with a link to the formal publication through the relevant DOI), provides a link to the license, indicates if changes were made, and the licensor is not represented as endorsing the use made of the work. The authors hold the copyright for their published work on the Tikrit J. Pure Sci. website, while Tikrit J. Pure Sci. is responsible for appreciate citation of their work, which is released under CC-BY-4.0, enabling the unrestricted use, distribution, and reproduction of an article in any medium, provided that the original work is properly cited.
References
[1] Ozaki, T. and Oda, H., (1977), "Nonlinear Time Series Models Identification by Akaike's Information Criterion", In Information and Systems, ed. Dubuisson . Pergamum Press, Oxford. pp(83-91) .
[2] Priestley, M.B., (1988), "Nonlinear And Nonstationary Time Series Analysis" London: ACADEMIC. Press.
[3] Mohammad, A. A. and Salim, A. J., (2007), "Stability of logistic autoregressive model" , Qatar University, 27:17-28.
[4] Salim, A. J. and Ahmad, A. A., (2018) , "Stability of a Non-Linear Exponential Autoregressive Model" , Open Access Library Journal , Vol.(05) , No.(04) , PP (1-15) .
[5] Salim, A. J. and Youns, A. S., (2019), "Study of Stability of Non-linear Model with Hyperbolic Secant Function" , J. Edu. & Sci., Vol. (28), No. (1), PP (106-120).
[6] Mohammad, A. A., Hamdi, O. A., Khaleel, M. A. " On stability Conditions of Pareto Autoregressive model" , Tikrit Journal of Pure Science, Vol.(25), No.(5), pp(93-98), 2020 .
[7] Pollard, J. H., & Valkovics, E. J. (1992), "The Gompertz distribution and its applications" , Genus, Vol.48, No. 3, PP. 15-28.
[8] Sanku Dey, Fernando A. Moala & Devendra Kumar, "Statistical properties and different methods of estimation of Gompertz distribution with application" , Journal of statistics & management systems, 21(5), PP (839-876), 2018.
[9] Tong, H., (1990), "Nonlinear Time Series: A Dynamical System Approach" , Oxford University Press, New York.
[10] Ozaki, T., (1982), "The statistical Analysis of perturbed limit cycle processes using Nonlinear Time Series Models" , Journal of Time Series Analysis, Vol.1, pp (29-41).
[11] Ozaki, T., (1985), "Nonlinear Time Series Models and Dynamical Systems", Handbook of Statistics , V. 5 (Ed. Hannan , E. J. and Krishnailah , P. R. and Rao , M. M. ) , Elsevier Science Publishers B. V. , pp (25-83) .
[12] Mohammad, A. A., Noori, N. A., "Dynamical Approach in studying GJR-GARCH (Q, P) Models with Application" , Tikrit Journal of Pure Science, 26(2), 2021.