2015/06/30 by Fangjian Guo, Dan Yang, Zimo Yang +2
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Applied mathematics #Autocorrelation #Complex Network Analysis Techniques #Complex Systems and Time Series Analysis #Computer science #Exponent #Gaussian #Law #Mathematical analysis #Mathematics #MovieLens #Opinion Dynamics and Social Influence #Physics #Power law #Quantum mechanics #Series (stratigraphy) #Statistical physics #Statistics #Upper and lower bounds #physics.data-an #physics.soc-ph
paper · pdf · doi:10.1103/physreve.95.052314
published as Phys. Rev. E 95, 052314 (2017) · 10 pages, 4 figures (revised)
arxiv created 2017/04/28 · openalex publication_date 2017/05/19 · arxiv updated 2017/05/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Many time series produced by complex systems are empirically found to follow power-law distributions with different exponents α. By permuting the independently drawn samples from a power-law distribution, we present nontrivial bounds on the memory strength (first-order autocorrelation) as a function of α, which are markedly different from the ordinary ±1 bounds for Gaussian or uniform distributions. When 1<α≤3, as α grows bigger, the upper bound increases from 0 to +1 while the lower bound remains 0; when α>3, the upper bound remains +1 while the lower bound descends below 0. Theoretical bounds agree well with numerical simulations. Based on the posts on Twitter, ratings of MovieLens, calling records of the mobile operator Orange, and the browsing behavior of Taobao, we find that empirical power-law-distributed data produced by human activities obey such constraints. The present findings explain some observed constraints in bursty time series and scale-free networks and challenge the validity of measures such as autocorrelation and assortativity coefficient in heterogeneous systems.