Proceedings of the National Academy of Sciences· 2026Q1
Generalized Taylor’s law for infinite-mean heavy-tailed data under dependence and heterogeneity
- 1citations
- Q1SCImago
- 2026year
Short summary
A generalized Taylor's law is established for heavy-tailed data with infinite means, accommodating dependence and heterogeneity, extending its applicability to time series and network data.
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Key points
- Taylor's law, relating variance to mean via a power-law, is generalized for heavy-tailed distributions with infinite means.
- The generalization accommodates dependent and heterogeneous data, relaxing previous independence assumptions.
- Probabilistic limits and convergence rates are established for this generalized law.
- The findings enable Taylor's law to be applied to dependent time series and network-structured data.
AI-generated from the title and abstract; the full text is not read.
Abstract
Taylor's law, also known as fluctuation scaling in physics and the power-law variance function in statistics, is an empirical pattern widely observed across fields including ecology, physics, finance, and epidemiology. It states that the variance of a sample scales as some power of the mean of the sample. We study generalizations of Taylor's law in the context of heavy-tailed distributions with infinite mean and variance. We establish the probabilistic limit and analyze the associated convergence rates. Our results extend the existing literature by relaxing the assumption that the observed random variables are independently and identically distributed to accommodate dependence and heterogeneity among them. This generalization enables application of Taylor's law to dependent time series and network-structured data. We support the theoretical developments by extensive simulations, and the practical relevance through applications to real network data.
The authors' abstract, as published at the source. Proceedings of the National Academy of Sciences, 2026 · DOI ↗
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Field: Economics and Econometrics
Economics and EconometricsEconomics, Econometrics and Finance