While a massive amount of time series can now be collected in many physical systems, it is a challenge to build an analytic model that can correctly profile the data because those time series usually exhibit various behaviors. In this paper we propose an integrated method to address the heterogeneity issue in modeling big time series data. We first extracts relevant features to summarize the underlying dynamics of those series. We present both linear and nonlinear feature extraction techniques, as well as a procedure to determine the right extraction method for individual time series. Given extracted features, our method further models the trajectory pattern of time series in the feature space. Both a regression based and a density based method are presented to profile different types of feature trajectories. Experimental results in a real power plant illustrate that our feature extraction and trajectory model are effective to profile various time series. Our method has been used to successfully detect anomalies in the system.