2019/07/31 by Claude Godrèche, J. M. Luck, Jean-Marc Luck · 1 citation
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Complex Systems and Time Series Analysis #Distribution (mathematics) #Exponent #Exponential distribution #Exponential function #Financial Risk and Volatility Modeling #Geometry #Independent and identically distributed random variables #Mathematical analysis #Mathematics #Moving average #Physics #Power law #Probability and statistics #Random variable #Scaling #Sequence (biology) #Series (stratigraphy) #Statistical Mechanics and Entropy #Statistical physics #Statistics #cond-mat.stat-mech #math-ph #math.MP #math.PR
paper · pdf · doi:10.1088/1742-5468/ab5d08
published in Journal of Statistical Mechanics Theory and Experiment 2020(2), 023201 (Institute of Physics) · 37 pages, 6 figures
arxiv created 2019/11/06 · openalex publication_date 2020/02/01 · arxiv updated 2021/01/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Abstract We investigate how the statistics of extremes and records is affected when taking the moving average over a window of width p of a sequence of independent, identically distributed random variables. An asymptotic analysis of the general case, corroborated by exact results for three distributions (exponential, uniform, power-law with unit exponent), evidences a very robust dichotomy, irrespective of the window width, between superexponential and subexponential distributions. For superexponential distributions the statistics of records is asymptotically unchanged by taking the moving average, up to interesting distribution-dependent corrections to scaling. For subexponential distributions the probability of record breaking at late times is increased by a universal factor R p , depending only on the window width.