Identifying Ordinal Similarities at Different Temporal Scales

This study implements the permutation Jensen--Shannon distance as a metric for discerning ordinal patterns and similarities across multiple temporal scales in time series data. Initially, we present a numerically controlled analysis to validate the multiscale capabilities of this method. Subsequently, we apply our methodology to a complex photonic system, showcasing its practical utility in a real-world scenario. Our findings suggest that this approach is a powerful tool for identifying the precise temporal scales at which two distinct time series exhibit ordinal similarity. Given its robustness, we anticipate that this method could be widely applicable across various scientific disciplines, offering a new lens through which to analyze time series data.