عملية غير انعكاسية- عمية ضوضاء متكامل نسبياً- تقريب الانحدار الذاتي- معادلات Yule- Walker- طريقة اقل المربعات- طيقة الامامية- الخلفية – طريقتي Burg.
                                                        
                                                                                                                                                                                                                                                                                                            
                                                            non-invertible process
                                                        
                                                                                                            
                                                            fractionally- integrated noise process
                                                        
                                                                                                            
                                                            autoregressive   approximation
                                                        
                                                                                                            
                                                            Yule-Walker equations
                                                        
                                                                                                            
                                                            Least Squares
                                                        
                                                                                                            
                                                            Least Squares ( forward- backword )  and   Burg’s methods.
                                                        
                                                                                                                                                                                         
                                                                        
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                                        Abstract
      In this study, we compare between the autoregressive approximations (Yule-Walker equations, Least Squares , Least Squares ( forward- backword ) and Burg’s (Geometric and Harmonic ) methods, to determine the optimal approximation to the time series generated from the first - order moving Average non-invertible process, and fractionally - integrated noise process, with several values for d (d=0.15,0.25,0.35,0.45) for different sample sizes (small,median,large)for two processes . We depend on figure of merit function which proposed by author Shibata in 1980, to determine the theoretical optimal order according to min
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