Time series analysis is in predictive modeling and decision-making across numerous disciplines. A key challenge involves identifying similar intervals that reveal critical patterns and inform strategic decisions. This paper introduces the Finding Best Similar (FBS) method, a framework for time series comparison that prioritizes distribution-based similarity over traditional point-to-point alignment. FBS employs Kernel Density Estimation (KDE) to model the underlying statistical distributions of time series segments and evaluates their differences using measures such as Kullback–Leibler Divergence, Rényi’s Divergence, Jensen-Shannon Divergence, and Hellinger Distance. By focusing on probability distributions rather than time-indexed values, FBS offers robustness against noise, scaling, and temporal misalignment. Utilizing a sliding window approach, FBS efficiently detects intervals with similar distributions, enabling both short- and long-term insights. Experimental results demonstrate that FBS achieves the highest future correlation of 0.898, signifying a 1.4% improvement over other methods, with statistically significant results underscoring its reliability in practical applications. In particular, the concept of Predictive Fidelity highlights how certain stocks exhibit consistent recurring patterns: FBS excels at uncovering these resemblances and correlating them with future price movements. By bypassing the need for elastic alignment, FBS remains computationally scalable and suitable for large datasets. Its adaptability is further underscored by diverse applications, including anomaly detection, pattern recognition, forecasting, and financial time series. Together, these findings establish FBS as a robust, domain-agnostic grounded solution for extracting meaningful insights from temporal data while offering a direct measure of how effectively a series replicates-and potentially predicts-its own past.

Keywords