Fractal and multifractal descriptors restore ergodicity broken by non-Gaussianity in time series

Ergodicity breaking is a challenge for biological and psychological sciences. necessary condition linear causal modeling. Long-range correlations non-Gaussianity characterizing various measurements break ergodicity routinely, threatening our capacity (e.g., in fractional Gaussian noise, a.k.a. "pink noise") ergodicity--in raw series, as well some but not all standard descriptors of variability, i.e., coefficient variation (CV) root mean square (RMS) deviation (SD) longer series. The present work demonstrates that progressive increases conspire with long-range to SD series lengths. Meanwhile, explicitly encoding the cascade dynamics can generate temporally correlated non-Gaussian noise offers way restore models. Specifically, fractal multifractal properties encode both scale-invariant power-law their variety, respectively, which features index underlying parameters. Fractal processes show no hence, provide more stable explanation form processes. offer path restoring modeling these fields.