A detection analysis for temporal memory patterns at different time-scales

This paper introduces a novel methodology that utilizes latency to unveil time-series dependence patterns. A customized statistical test detects memory dependence in event sequences by analyzing their inter-event time distributions. Synthetic experiments based on the renewal-aging property assess the impact of observer latency on the renewal property. Our test uncovers memory patterns across diverse time scales, emphasizing the event sequence's probability structure beyond correlations. The time series analysis produces a statistical test and graphical plots which helps to detect dependence patterns among events at different time-scales if any. Furthermore, the test evaluates the renewal assumption through aging experiments, offering valuable applications in time-series analysis within economics.