Studying the Stability of Some Models Combinatory with Application

In this paper we find the statistical properties (Moments) of the harmonic model with additive noise, The stability of the mixed spectra (linear and non-linear models) for special case (low order) by using the Ozaki linear approximation method is found .The time series of the mean monthly temperature of Bege City is applied in order to explain the studied method. A mathematical model SARIMA(1,0,0)(2,0,0)s is suggested by the NBIC criterion and other statistical tools (auto-correlation and the residual variance). A one year ahead prediction is made for the studied time series by using the proposed model .