Abstract: A doubly time series model is defined to satisfy the relation X_t-A₀=（θ_t+α）X_t-1+α_t whereθ_g:t=0,1,2,…is itself a stochastic series,andα_t:t=0,1,2…is white noise with Eα_t²=σ²..Whenθ_t:t=0,1,2,…satisfy AR（1）or MA（1）model,this paper gives out poly-steps minimum mean square error forecast ofX_t,t=0,1,2…, and the comparison of its properties with updated linear minimum mean square error forecasted by computer simulation.