Most algorithms for mining or indexing time series data do not operate directly on the original data, but instead they consider alternative representations that include transforms, quantization, approximation, and multiresolution abstractions. Choosing the best representation and abstraction level for a given task/dataset is arguably the most critical step in time series data mining. In this paper, we investigate techniques that discover the natural intrinsic representation model, dimensionality and alphabet cardinality of a time series. The ability to discover these intrinsic features has implications beyond selecting the best parameters for particular algorithms, as characterizing data in such a manner is useful in its own right and an important sub-routine in algorithms for classification, clustering and outlier discovery. We will frame the discovery of these intrinsic features in the Minimal Description Length (MDL) framework. Extensive empirical tests show that our method is simpler, more general and significantly more accurate than previous methods, and has the important advantage of being essentially parameter-free.