Quantifying predictive knowledge: Wavelet energy alfa-divergence measure for time series uncertainty reduction

Understanding the relationship between time series is essential for predictive modeling and decision-making in several domains. In this article, we introduce and demonstrate the properties of a novel measure derived from wavelet and alfa-divergence, namely wavelet energy alfa-divergence measure. Unlike other traditional wavelet entropy energy-based measures, which primarily serve to assess the inherent predictability of one time series, this new measure takes into account pairs of time series and it reveals how the knowledge of one series can reduce uncertainty in another series across the time as well as the frequency domain. Specifically, our measure can indicate to which extent we can extract information content from one series that is related to the second series. This analysis is performed for both low and high-frequency events by varying the order parameter alfa of the divergence, and for both short and long-run by analyzing the scale value of the wavelet. Moreover, we apply the method to a real-world dataset highlighting the impact of this measure.