Abstract: A time series model for the multi―step prediction is proposed in the paper. Having calculated mean generating functions of the time series and its difference and then screening all extending series of the mean generating functions with the couple score criterion, the model which is well available for both the fitting and the forecast is built. As an example, total precipitation during the period from June to August over the lower and middle reaches of the Yangtse river is modeled. It is shown that the model proposed here is useful for year―to―year climate prediction or month―to―month long―range weather forecast