Efficient Computation of All-Window Length Correlations

Adam Charane, Matteo Ceccarello, Anton Dignös, Johann Gamper

Abstract: The interactive exploration of time series is an important task in data analysis. In this paper, we concentrate on the investigation of linear correlations between time series. Since the correlation of time series might change over time, we consider the analysis of all possible subsequences of two time series. Such an approach allows identifying, at different levels of window length, periods over which two time series correlate and periods over which they do not correlate. We provide a solution to compute the correlations over all window lengths in $$O(n^2)$$ time, which is the size of the output and hence the best we can achieve. Furthermore, we propose a visualization of the result in the form of a heatmap, which provides a compact overview on the structure of the correlations amenable for a data analyst. An experimental evaluation shows that the tool is efficient to allow for interactive data exploration.