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 minimum value for Figure of merit functio, for several values for h (h=1 to) to compare between estimation methods which used in this study. Also we based On Information Criteria which imply (Akaike, Final Prediction Error, Mallow , s statistic, Parzen , Bhansali). Addition to several Criteria based on values for estimation parameters such as Mean Error Estimation ( MEE ), Mean Square Error Estimation ( MSEE ) and Mean Absolute Error Estimation ( MAEE ) .The results are obtained by using simulation which is based on Matlab programms.
