Abstract: Full autoregressive models are always characterize by many parameters and this is a problem. Some of these parameters are redundant that is close to zero and there is the need to eliminate these parameters through the concept of subsetting. Subsets autoregressive models are free from redundant parameters thereby lowering the residual variance and forecasting with such models will always give a better forecast. Likewise auto projective models calculate on the basis of current knowledge what the errors would have been which gives us some guide to errors of the future. It is in the light of the above we considered the subsets autoregressive models and auto projective models, to see how these models will perform with regard to forecast. Exponential smoothening was used to forecast the future value in auto projective models while conditional least square predictor was used to forecast the future value in subset autoregressive models. An algorithm was proposed to eliminate redundant parameters from the full order autoregressive models and the parameters were estimated. To determine optimal models, residual variance, Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) were adopted. Results revealed that the residual variance attached to the subset autoregressive models is smaller than the residual variance attached to the auto projective models. We conclude that the forecast for subset autoregressive is preferred to the forecast for auto projective.