A two time step stochastic multi-variables multi-sites hydrological data forecasting model was developed and verified using a case study. The philosophy of this model is to use the cross-variables correlations, cross-sites correlations and the two steps time lag correlations simultaneously, for estimating the parameters of the model which then are modified using the mutation process of the genetic algorithm optimization model. The objective function that to be minimized is the Akiake test value. The case study is of four variables and three sites. The variables are the monthly air temperature, humidity, precipitation, and evaporation; the sites are Sulaimania, Chwarta, and Penjwin, which are located north Iraq. The model performance was checked by comparing it's results with the results of six forecasting models developed for the same data by Al-Suhili and khanbilvardi, 2014.The check of the performance of the new developed model was made for three forecasted series for each variable, using the Akaike test which indicates that the developed model is more successful, since it gave the minimum (AIC) values for (91.67 %) of the forecasted series. This indicates that the developed model had improved the forecasting performance. For the rest of cases (8.33%), other models gave the lowest AIC value, however it is slightly lower than that given by the developed model. Moreover the t-test for monthly means comparison between the models indicates that the developed model has the highest percent of succeed (100%).
