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Time series data are widely used in many applications including critical decision support systems. The goodness of the dataset, called the Fitness of Use (FoU), used in the analysis has direct bearing on the quality of the information and knowledge generated and hence on the quality of the decisions based on them. Unlike traditional quality of data which is independent of the application in which it is used, FoU is a function of the application. As the use of geospatial time series datasets increase in many critical applications, it is important to develop formal methodologies to compute their FoU and propagate it to the derived information, knowledge and decisions. In this paper we propose a formal framework to compute the FoU of time series datasets. We present three different techniques using the Dempster-Shafer belief theory framework as the foundation. These three approaches investigate the FoU by focusing on three aspects of data: data attributes, data stability, and impact of gap periods, respectively. The effectiveness of each approach is shown using an application in hydrological datasets that measure streamflow. While we use hydrological information analysis as our application domain in this research, the techniques can be used in many other domains as well.