Rescaled Range Analysis of Interval-Valued Time Series

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.