A novel hybrid method for time series subsequence join

The exact method JOCOR, proposed by Mueen et al., is the first method for joining two time series on subsequence correlation. Although JOCOR requires the time complexity O(n
²
lgn), where n is the length of the time series, it is still time-consuming even for medium-size time series. In this paper, we propose a hybrid method which can run faster than JOCOR. Our method consists of four main steps. First, a list of subsequences is extracted from the raw time series based on important extrema. Second, we apply a nested loop join using a sliding window and Dynamic Time Warping distance to find all the matching subsequences in the two time series. Third, we concatenate all matching subsequences whose indexes are adjacent into longer ones and find the pair of subsequences which has the smallest distance between them. Finally, we apply JOCOR to find the most correlated segments in the two time series. In comparison to JOCOR, our hybrid method performs much faster while high accuracy is guaranteed.