Considering the randomness of homogeneous out-growth function ,the new criterion for screening factors is used in the period analysis and an improved scheme of stepwise regression is brought out.From the case computations, such as the sea surface temperature in the equatorial Eastern Pacific area,the precipitation over the regions along Changjiang River and in southern China during the rainy scaso,n,the sunspot and the tree ring index,it is found that the scheme is not only suitable for long-term prediction but also capable of detecting the potential periods in a time series.