The majority of existing spectrum prediction models in Cognitive Radio Networks (CRNs) don't fully explore the hidden correlation among adjacent observations. In this paper, we first develop a novel prediction approach termed high-order hidden bivariate Markov model (H 2 BMM) for a stationary CRN. The proposed H 2 BMM leverages the advantages of both HBMM and high-order, which applies two dimensional parameters, i.e., hidden process and underlying process, to more accurately describe the channel behavior. In addition, the current channel state is predicted by observing multiple previous states. Afterwards, the mobility of secondary users is fully considered and we propose an advanced approach based on H 2 BMM, termed Advanced H 2 BMM, to accommodate a mobile CRN. Extensive simulations are conducted and results verify that the prediction accuracy is significantly improved using the proposed (H 2 BMM. The Advanced H 2 BMM is also evaluated with comparison to H 2 BMM and results show considerable improvements of H 2 BMM in a mobile environment.