Finding Maximal Significant Linear Representation between Long Time Series

In some applications on time series data, finding linear correlation between time series is important. However, it is meaningless to measure the global correlation between two long time series. Moreover, more often than not, two time series may be correlated in various segments. To tackle the challenges in measuring linear correlation between two long time series, in this paper, we formulate the novel problem of finding maximal significant linear representation. The major idea is that, given two time series and a quality constraint, we want to find the longest gapped time interval on which a time series can be linearly represented by the other within the quality constraint requirement. We develop a point-based approach, which exploits a novel representation of linear correlation between time series on segments, and transforms the problem into geometric search. We present a systematic empirical study to verify its efficiency and effectiveness.