Abstract
The present research aims to estimate of the spectral density function of the non-stationary time-series of( Uniformly Modulated Processes) (mup) model, when Z represents the model AR (1), AR (2), and ARMA (1,1) with various parameters. These methods are the (evolutionary spectral method),( Wigner- Vill method) and the( short-time period gram method). In order to make use of the properties of the three methods, shrinking principle has been adopted among the estimation of the properties of the three methods is called (Shrinkage Method) and compares them together using the criteria (Mean Integrated Square Error) (MISE). The most important conclusion which has been reached by the present research is that the best method to estimate the function of the spectral density is the Shrinkage one suggested by ARMA (1,1) model in adding the sizes of the three samples, the model MA (1) at θ1= 0.5 and the model AR (1) at Φ1= 0.9, while the two methods, Sh. Pe.S and Sh. Me. S of the model AR (2) at all sizes at the parameters Φ1= 0.4 and Φ2= 0.3, Φ1=0.8, and Φ2=-0.4.
