Efficient time series similarity search is a fundamental operation for data exploration and analysis. While previous work has focused on indexing progressively larger datasets and has proposed data structures with efficient exact search algorithms, we motivate the need for approximate query methods that can be used in interactive exploration and as fast data analysis subroutines on large spatiotemporal datasets. This thesis formulates a simple approximate range query problem for time series data, and proposes a method that aims to quickly access a small number of high-quality results of the exact search resultset. We formulate an anytime framework, giving the user flexibility to return query results in arbitrary cost, where larger runtime incrementally improves search results. We propose an evaluation strategy on each query framework when the false dismissal class is very large relative to the query resultset and investigate the performance of indexing novel classes of time series subsequences.