We address the problem of capturing and tracking local correlations among time evolving time series. Our approach is based on comparing the local auto-covariance matrices (via their spectral decompositions) of each series and generalizes the notion of linear cross-correlation. In this way, it is possible to concisely capture a wide variety of local patterns or trends. Our method produces a general similarity score, which evolves over time, and accurately reflects the changing relationships. Finally, it can also be estimated incrementally, in a streaming setting. We demonstrate its usefulness, robustness and efficiency on a wide range of real datasets.