In this paper, we formulate a novel time series representation framework that captures the inherent data dependency of time series and that can be easily incorporated into existing statistical classification algorithms. The impact of the proposed data representation stage in the solution to the generic underlying problem of time series classification is investigated. The proposed framework, which we call structural generative descriptions moves the structural time series representation to the probability domain, and hence is able to combine statistical and structural pattern recognition paradigms in a novel fashion. Two algorithm instantiations based on the proposed framework are developed. The algorithms are tested and compared using different publicly available real-world benchmark data. Results reported in this paper show the potential of the proposed representation framework, which in the experiments investigated, performs better or comparable to state-of-the-art time series description techniques.