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To achieve effective load balancing and a robust Grid environment, extended load forecast for computational resources is increasingly required. Thus, this paper proposes a method of predicting network and CPU load variance within a wide range, from several minutes to over a week. This is the widest range of prediction of the existing algorithms in the load of computational resources for the Grid environment. The distinctiveness of our algorithm is in using seasonal load variation for both load variance and one-step-ahead prediction. We apply seasonal fluctuation in CPU load to network load variation especially for network load variance prediction. Furthermore, the Markov model-based meta-predictor is used for one-step-ahead prediction, which is sensitive to late trends. The results of the experiments demonstrate that our algorithm gives a good curve for expected 8-day-long load variance, and makes accurate one-step-ahead predictions. The mean error rate for one-step-ahead predictions is 9.4% in the case of network load, and 6.2% in the case of CPU load. Moreover, the least mean error rate for wider range forecasts is 5.5% for network load variation, and 3.6% for CPU load variation.