1. A stream data processing method for processing a stream which is a flow of time series data including plural data tuples to which each time stamp is applied and which are continuously incoming in the ascending order of time stamps, and for applying an index to each data tuple of the stream, said method comprising the steps of: subsequent to an index-applying process for preceding data tuple, computing a first index rating an incoming data tuple of the stream, as an objective data tuple, according to index function algorithm utilizing the objective data tuple and the preceding data tuple of the stream in predetermined period of time; associating the first index with the incoming data tuple; processing the objective data tuple according to a registered query; acquiring an interim index based upon the first index associated with the objective data tuple and a final index which is stored for the preceding data tuples; outputting the processed data tuple and the acquired interim index as an index rating the processed data tuple; at a moment when a following data tuple arrives, computing, by using at least the following data tuple, a second index rating said objective data tuple; and storing the second index associated with the objective data tuple as a final index rating the objective data tuple.