A randomization test for the comparison of ordered sequences

Several algorithms, based on dynamic programming techniques, for comparing, matching, or cross-correlating two ordered sequences of observations now exist. All such algorithms produce one or more optimal matchings, no matter what data are used. This paper presents an empirical method, based on a randomization test, for assessing how well the given sequences are matched or slotted together. The randomization test is designed to test the assumption, implicit in most cross-correlation algorithms, that both sequences comprise observations, at unknown but ordered times, from the same underlying yet unknown function of time. The test is intuitively appealing, easy to implement, works well on both artificial and real data, and requires no complicated parametric modelling.