In many applications, the data of interest comprises multiple sequences that evolve over time. Examples include currency exchange rates, network traffic data. We develop a fast method to analyze such co-evolving time sequences jointly to allow (a) estimation/forecasting of missing/delayed/future values, (b) quantitative data mining, and (c) outlier detection.Our method, MUSCLES, adapts to changing correlations among time sequences. It can handle indefinitely long sequences efficiently using an incremental algorithm and requires only small amount of storage and less I/O operations. To make it scale for a large number of sequences, we present a variation, the Selective method and propose an efficient algorithm to reduce the problem size.Experiments on real datasets show that outperforms popular competitors in prediction accuracy up to 10 times, and discovers interesting correlations. Moreover, Selective scales up very well for large numbers of sequences, reducing response time up to 110 times over MUSCLES, and sometimes even improves the prediction quality.