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In this paper we revisit the problem of decomposing a signal into a tendencyand a residual. The tendency describes an executive summary of a signal thatencapsulates its notable characteristics while disregarding seemingly random,less interesting aspects. Building upon the Intrinsic Time Decomposition (ITD)and information-theoretical analysis, we introduce two alternative proceduresfor selecting the tendency from the ITD baselines. The first is based on themaximum extrema prominence, namely the maximum difference between extremawithin each baseline. Specifically this method selects the tendency as thebaseline from which an ITD step would produce the largest decline of themaximum prominence. The second method uses the rotations from the ITD andselects the tendency as the last baseline for which the associated rotation isstatistically stationary. We delve into a comparative analysis of theinformation content and interpretability of the tendencies obtained by ourproposed methods and those obtained through conventional low-pass filteringschemes, particularly the Hodrik-Prescott (HP) filter. Our findings underscorea fundamental distinction in the nature and interpretability of thesetendencies, highlighting their context-dependent utility with emphasis inmulti-scale signals. Through a series of real-world applications, wedemonstrate the computational robustness and practical utility of our proposedtendencies, emphasizing their adaptability and relevance in diverse time seriescontexts.

Estimating an Executive Summary of a Time Series: The Tendency