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In this paper, we address the issue of forecasting for periodically measured nonstationary traffic based on statistical time series modeling. Often with time-series-based applications, minimum-mean-square error-based forecasting is sought that minimizes the square of the positive, as well as the negative, deviations of the forecast from the unknown true value. However, such a forecast function is not directly applicable for applications such as predictive bandwidth provisioning in which the negative deviations (underforecast) have more impact on the system performance than the positive deviation (overforecast). For instance, an underforecast may potentially result in an insufficient allocation of bandwidth leading to short-term data loss. To facilitate a differential treatment between the under- and the over-forecast, we introduce a generalized forecast cost function that is defined by allowing a different penalty associated with the under and the overforecast. We invoke mild assumptions on the first-order characteristics of such penalty functions to ensure the existence and uniqueness of the optimal forecast value in the domain of interest. The sufficient condition on the forecast distribution is that all the orders of the moments are well defined. We provide several possible classes of penalty functions to illustrate the generic nature of the cost function and its applicability from a dynamic bandwidth provisioning perspective. A real network traffic example using several classes of penalty functions is presented to demonstrate the effectiveness of our approach.