For tracing tag locations, the trajectories should be modeled and indexed in radio frequency identification (RFID) systems. The trajectory of a tag can be represented as a line that connects two spatiotemporal locations captured when the tag enters and leaves the vicinity of a reader. If a tag enters but does not leave a reader, its trajectory is represented only as a point captured at entry. Because the information that a tag stays in a reader is missing from the trajectory represented only as a point, it is impossible to find the tag that remains in a reader. To solve this problem we propose the data model in which trajectories are defined as time-parameterized intervals and new index scheme called the Time Parameterized Interval R-tree. We also propose new insert and split algorithms that reduce the area of nodes to enable efficient query processing. We evaluate the performance of the proposed index scheme and compare it with previous indexes on various datasets.