Cognitive radio communications depend on methods for sensing the spectrum as well as adapting transmission parameters to available resources. In this context, this work proposes a novel system that makes use of prediction to dynamically allocate subcarriers to different transmissions in an orthogonal frequency division multiplexing (OFDM) system. To this end, the proposal is comprised of a predictive component which makes use of a neural network and multiresolution analysis and a second component, which uses wavelet analysis and cognitive radio functions to carry out a dynamic allocation of subcarriers in an OFDM system. The use of wavelets allows the system to split the data stream in blocks of information to be transmitted over multiple orthogonal subcarriers. This proposed system makes use of the decision‐making functions of a cognitive radio device to select the number and position of the subcarriers used for communications without interference. Although there exist other OFDM systems using wavelets, they are not used in combination with the decision‐making functions implemented in cognitive radio devices. In contrast, the proposed OFDM system operates using some of these functions, thus being able to better adapt its operational parameters. The use of wavelets combined with a neural network model improves the prediction of the bandwidth utilization as shown in this work. It is concluded that the proposed system improves spectral efficiency and data rate by using the decision‐making functions of cognitive radios to select the appropriate OFDM subcarriers to be used during the data transmissions.