Category: Statistics

Summary: Testing how stronger temporal correlation changes persistence statistics in a random multiplicative process by comparing extreme values, tail mass, and growth slope across correlation levels.

Random multiplicative processes can look similar in the mean while differing sharply in how often they generate persistent extreme outcomes. This experiment asks how increasing correlation strength reshapes that persistence, with particular focus on the upper tail and the growth of large excursions.

The script simulates the process across a fixed set of correlation values and compares the highest normalized magnitude, tail averages, and a fitted growth slope between weakly and strongly correlated cases. The analysis then summarizes how those observables shift from low to high correlation over repeated trials.

That framing matters because persistence is not captured by one summary number alone. By tracking both extremes and tail-shape changes, the experiment looks for systematic ways in which correlated multiplicative noise creates longer-lived or more concentrated rare events.

Method: Repeated simulations of a correlated random multiplicative process across several correlation strengths, with tail and extreme-value comparisons between low and high correlation.

What is measured: Change in maximum normalized magnitude, change in tail mean, change in growth slope, and low- versus high-correlation persistence statistics.