In this paper, we propose a model-based bandwidth prediction scheme for variable-bit-rate (VBR) video traffic with regular group of pictures (GOP) pattern. Multiplicative ARIMA process called GOP ARIMA (ARIMA for GOP) is used as a base stochastic model, which consists of two key ingredients: prediction and model validity check. For traffic prediction, we deploy a Kalman filter over GOP ARIMA model, and confidence interval analysis for validity determination. The GOP ARIMA model explicitly models inter and intra-GOP frame size correlations and the Kalman filter-based prediction maintains "state" across the prediction rounds. Synergy of the two successfully addresses a number of challenging issues, such as a unified framework for frame type dependent prediction, accurate prediction, and robustness against noise. With few exceptions, a single video session consists of several scenes whose bandwidth process may exhibit different stochastic nature, which hinders recursive adjustment of parameters in Kalman filter, because its stochastic model structure is fixed at its deployment. To effectively address this issue, the proposed prediction scheme harbors a statistical hypothesis test in the prediction framework. By formulating the confidence interval of a prediction in terms of Kalman filter components, it not only predicts the frame size but also determines validity of the stochastic model. Based upon the results of the model validity check, the proposed prediction scheme updates the structures of the underlying GOP ARIMA model. We perform a comprehensive performance study using publicly available MPEG-2 and MPEG-4 traces. We compare the prediction accuracy of four different prediction schemes. In all traces, the proposed model yields superior prediction accuracy than the other prediction schemes. We show that confidence interval analysis effectively detects the structural changes in the sample sequence and that properly updating the model results in more accurate prediction. However, model update requires a certain length of observation period, e. g., 60 frames (2 s). Due to this learning overhead, the advantage of model update becomes less significant when scene length is short. Through queueing simulation, we examine the effect of prediction accuracy over user perceivable QoS. The proposed bandwidth prediction scheme allocates less 50% of the queue(buffer) compared to the other bandwidth prediction schemes, but still yields better packet loss behavior.