Studying the Stability of a Non-linear Autoregressive Model (Polynomial with Hyperbolic Cosine Function) | Zendy

Abdulghafoor Salim | Zendy; Anas Youns AL-Mashhdanny | Zendy

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Studying the Stability of a Non-linear Autoregressive Model (Polynomial with Hyperbolic Cosine Function)

Author(s) -

Abdulghafoor Salim,

Anas Youns AL-Mashhdanny

Publication year - 2014

Publication title -

maǧallaẗ al-rāfidayn li-ʿulūm al-ḥāsibāt wa-al-riyāḍiyyāẗ/al-rafidain journal for computer sciences and mathematics

Language(s) - English

Resource type - Journals

eISSN - 2311-7990

pISSN - 1815-4816

DOI - 10.33899/csmj.2014.163733

Subject(s) - autoregressive model , mathematics , linearization , limit cycle , stability (learning theory) , limit (mathematics) , hyperbolic function , polynomial , star model , trigonometric functions , mathematical analysis , singular point of a curve , nonlinear autoregressive exogenous model , function (biology) , nonlinear system , autoregressive integrated moving average , econometrics , computer science , statistics , time series , geometry , machine learning , evolutionary biology , biology , physics , quantum mechanics

In this paper we study the statistical properties of one of a non-linear autoregressive model with hyperbolic triangle function(polynomial with hyperbolic cosine function)by using the local linearization approximation method to find the stability of the model (singular point and its stability conditions and the stability of limit cycle).Where we started by the model of lower order (first and second and third order) and generalized the idea, and we tried to apply these theory results by using some of examples to explain one of important truth that says (if the model has unstable singular point, then it, maybe, has a stable limit cycle).

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