In this paper we propose a traffic predictor based on multiresolution decomposition for the adaptive bandwidth control in locally controlled self-sizing networks. A selfsizing network can provide quantitative packet-level QoS to aggregate traffic by allocating link/switch capacity automatically and adaptively using online traffic data. In a locally controlled network such as Internet, resource allocation decisions are made at the node level. We show that wavelet based adaptive bandwidth control method performs better than other popular methods like Gaussian predictor for such applications. We have compared the performance of different ortho-normal wavelets and found that Haar wavelet is best suited for traffic prediction. We have studied the effect of other wavelet parameters such as size of the window and number of filter coefficients. We also propose a novel adaptive wavelet predictor which can adapt very well to the changes of incoming bursty traffic.