On stability Conditions of Burr X Autoregressive model

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Zena. S. Khalaf
Azher. A. Mohammad

Abstract

This article deals with proposed nonlinear autoregressive model based on Burr X cumulative distribution function known as Burr X AR (p), we demonstrate stability conditions of the proposed model in terms of its parameters by using dynamical approach known as local linearization method to find stability conditions of a nonzero fixed point of the proposed model, in addition the study demonstrate stability condition of a limit cycle if Burr X AR (1) model have a limit cycle of period greater than one.

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How to Cite
Zena. S. Khalaf, & Azher. A. Mohammad. (2019). On stability Conditions of Burr X Autoregressive model. Tikrit Journal of Pure Science, 24(5), 91–96. https://doi.org/10.25130/tjps.v24i5.423
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References

[1] Tong, H. (1990). Nonlinear Time Series: A Dynamical System Approach, Oxford University Press, New York

[2] Ozaki, T. (1982). The Statistical Analysis of Perturbed Limit Cycle Processes Using Nonlinear Time Series Models. Journal of Time Series Analysis, Vol.3, N0.1, PP (29-41)

[3] Ozaki, T. (1985). Nonlinear Time Series Models and Dynamical Systems", Handbook of Statistics, Vol. S, Hannan, E. J. and Krishnailah, P.R. and Rao, M. M. . Elsevier Science Publishers R V., PP (25- 83).

[4] Mohammad A.A.; Salim A.J.(2007). Stability of Logistic Autoregressive Model. Qatar university of Science journal. Vol (27). PP (17-28)..

[5] Mohammad, A. A.; Gannam, A. K. (2010). Stability of Cauchy autoregressive model. Zanco journal of Pure and Applied Sci. – Sallahaddin University – Hawler (special Issue). pp(209-220)

[6] Salim A.J., Esmaeel k.; Jasim H. T. (2011). 'A study of the stability of an amplitude-dependent exponential autoregressive model with application", Iraqi Journal of Statistical Science, The Fourth Scientific Conference of the College of Computer Science & Mathematics. pp (52-62).

[7] Salim, A.J.; Youns, A. S. (2012). A Study of the Stability of a Non-Linear Autoregressive Models. Australian J. Basic Appl. Sci. 6 (13), pp (159–166). [8] Salim, A. G. J., Abdullah, A. S. Y. (2014). Studying the Stability of a Non-linear Autoregressive Model (Polynomial with Hyperbolic Cosine Function). AL-Rafidain Journal of Computer Sciences and Mathematics. 11(1), pp (81-91).

[9] Mohammad A. A.; Ghaffar M. K.(2016) . A study on stability of conditional variance for GARCH models with application. Tikrit journal of pure science. (4) 21.

[10] Raqab, M. Z. ; Kundu, D. (2006). Burr type X distribution: revisited. Journal of Probability and Statistical Sciences, 4(2), pp (179-193).

[11] Tarvirdizade, B.; Hossein K. G. (2015). Inference on Pr (X> Y) based on record values from the Burr Type X distribution. Hacettepe Journal of Mathematics and Statistics .v0l (45).1. pp(267-278).

[12] Ozaki, T. (1980). Non-linear time series models for non-linear random vibrations. Journal of Applied Probability, 17(1), pp (84-93), 1980.

[13] Haggan, V.; Ozaki, T. (1981). Modelling nonlinear random vibrations using an amplitude-dependent autoregressive time series model. Biometrika, 68(1),pp (189-196).

[14] Priestley M. B. (1981). Spectral Analysis and Time Series. Volume 1, univariate series. Academic Press Inc. London.