The federal communications commission (FCC) has predicted that, under the current regulatory environment, a spectrum shortage may be faced in the near future. This impending spectrum shortage is in part due to a rapidly increasing demand for wireless services and in part due to inefficient usage of currently licensed bands. A new paradigm pertaining to wireless spectrum allocation, known as cognitive radio (CR), has been proposed as a potential solution to this problem. This dissertation seeks to contribute to research in the field of CR through an investigation into the effect that a primary user (PU) channel occupancy model will have on the performance of a secondary user (SU) in a CR network. The model assumes that PU channel occupancy can be described as a binary process and a two state Hidden Markov Model (HMM) was thus chosen for this investigation. Traditional algorithms for training the model were compared with certain evolutionary-based training algorithms in terms of their resulting prediction accuracy and computational complexity. The performance of this model is important since it provides SUs with a basis for channel switching and future channel allocations. A CR simulation platform was developed and the results gained illustrated the effect that the model had on channel switching and the subsequently achievable performance of a SU operating within a CR network. Performance with regard to achievable SU data throughput, PU disruption rate and SU power consumption, were examined for both theoretical test data as well as data obtained from real world spectrum measurements (taken in Pretoria, South Africa). The results show that a trade-off exists between the achievable SU throughput and the average PU disruption rate. Significant SU performance improvements were observed when prediction modelling was employed and it was found that the performance and complexity of the model were influenced by the algorithm employed to train it. SU performance was also affected by the length of the quick sensing interval employed. Results obtained from measured occupancy data were comparable with those obtained from theoretical occupancy data with an average percentage similarity score of 96% for prediction accuracy (using the Viterbi training algorithm), 90% for SU throughput, 83% for SU power consumption and 71% for PU disruption rate.