Selection hyper-heuristics are optimisation methods that operate at the level above traditional (meta-)heuristics. Their task is to evaluate low level heuristics and determine which of these to apply at a given point in the optimisation process. Traditionally this has been accomplished through the evaluation of individual or paired heuristics. In this work, we propose a hidden Markov model based method to analyse the performance of, and construct, longer sequences of low level heuristics to solve difficult problems. The proposed method is tested on the well known hyper-heuristic benchmark problems within the CHeSC 2011 competition and compared with a large number of algorithms in this domain. The empirical results show that the proposed hyper-heuristic is able to outperform the current best-in-class hyper-heuristic on these problems with minimal parameter tuning and so points the way to a new field of sequence-based selection hyper-heuristics.