Key result
Extending rescaled-range analysis to interval-valued time series yields complementary complexity insights versus analyzing mean values.
Why the study?
Methods were needed to evaluate the scaling properties and complexity of interval-valued time series where signals take values in sets rather than single values.
The proposed extension of the rescaled-range analysis method to interval-valued time series provides complementary insights into the complexity of functional time series such as heart rate variability.
Offers complementary complexity metrics for cardiovascular time series; leaves open clinical validation and adoption.
This paper proposes an extension of the rescaled-range (R/S) analysis method from point-valued to Interval-Valued Time Series (ITS). The extension is based on specifying the distance between intervals and setting the cumulative time series for ITS. In this way, the resulting method evaluates the scaling properties of time series that combine complex variations of the mean value and intervals. The application of the proposed method to real-time series (Bitcoin price and heart rate variability) shows that interval analysis provides complementary insights on the complexity of time series to those obtained with the analysis of mean values. Overall, the present study should be seen as a step to characterize the complexity of functional time series where the signal does not have a single value but rather takes values in sets.
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Rodriguez et al. (2026) studied this question. Rescaled-range (R/S) analysis for Interval-Valued Time Series vs. Analysis of mean values was evaluated on Scaling properties of time series. An extension of the rescaled-range analysis method to interval-valued time series provided complementary insights on the complexity of time series compared to the analysis of mean values.
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