دراسة شروط استقرارية النموذج الأسى ذى الإنتقال الأملس للإنحدار الذاتى مع التطبيق - الدهمشى، هبة هانى عبدالله حسين; محمد، أزهر عباس (تكريت, 2008)
In this thesis we deals with studing of stability conditions of exponential smooth transition autoregressive model by using A dynamical approach based on a non linear dynamical systems Which known as a local linearization technique which it used by Ozaki(1985) in the study of stability conditions of the exponential autoregressive model . In this thesis we find stability conditions of the exponential smooth transition autoregressive model , we find a stability conditions of a non-zero singular point (if it exists)of the model and we put and prove of these conditions in theorem (3.2.1) , In addition we find a stability conditions of a limit cycle when the model posses a limit cycle and we put and prove these conditions in theorem (3.2.3) . In the fourth Chapter of this thesis we apply the conditions of the two above theorems on the data deals with the annual mean of sunspots , we modeling this data by using the exponential smooth transition autoregressive for the first ten orders, and we study the stability of each model , In addition we plot the trajectory of each model in order to ensure the convergence towards the non-zero singular point or a limit cycle of the studied model . Finally we make a stability Comparison between the exponential autoregressive models and the exponential Smooth transition autoregressive models. The Comparison results indicate that the exponential autoregressive model are best than the exponential smooth transition autoregressive models specially for the high orders . While this may be due to the structure of the used data .
Keywords: السلاسل الزمنية -- الإنحدار الذاتى -- النموذج الأسى -- الرياضيات