In order to increase spectrum utilization efficiency, CRs (Cognitive Radios) have been introduced to reuse white spaces left unused by legacy services under the strict constraint of not interfering them. In order to fulfill this constraint while optimising spectrum utilisation, it is important to get knowledge about primary-user activity in order to devise proper strategies for secondary-user operation. In this context, this paper proposes to strengthen Radio Environment Maps (REM) with statistical patterns of primary systems that capture among others temporal dependence structures between activity (ON) and inactivity (OFF) periods. Convergence times for the different statistics are analysed. Then, a set of novel spectrum selection criteria exploiting these statistics are proposed and assessed to benchmark the usefulness of primary statistical patterns retained in the REM. Results show that significant performance gains can be achieved in terms of a reduction in the number of required spectrum hand-overs. ; Peer Reviewed ; Postprint (published version)