We study the predictive power of autoregressive moving average models when forecasting demand in two shared computational networks, PlanetLab and Tycoon. Demand in these networks is very volatile, and predictive techniques to plan usage in advance can improve the performance obtained drastically. Our key finding is that a random walk predictor performs best for one-step-ahead forecasts, whereas ARIMA(1,1,0) and adaptive exponential smoothing models perform better for two and three-step-ahead forecasts. A Monte Carlo bootstrap test is proposed to evaluate the continuous prediction performance of different models with arbitrary confidence and statistical significance levels. Although the prediction results differ between the Tycoon and PlanetLab networks, we observe very similar overall statistical properties, such as volatility dynamics.