An Energy-Based Similarity Measure for Time Series

A new similarity measure, called SimilB, for time series analysis, based on the cross-ΨB-energy operator (2004), is introduced. ΨB is a nonlinear measure which quantifies the interaction between two time series. Compared to Euclidean distance (ED) or the Pearson correlation coefficient (CC), SimilB includes the temporal information and relative changes of the time series using the first and second derivatives of the time series. SimilB is well suited for both nonstationary and stationary time series and particularly those presenting discontinuities. Some new properties of ΨB are presented. Particularly, we show that ΨB as similarity measure is robust to both scale and time shift. SimilB is illustrated with synthetic time series and an artificial dataset and compared to the CC and the ED measures.