title: A dynamical systems explanation of the Hurst effect and atmospheric low-frequency variability.
abstract: The Hurst effect plays an important role in many areas such as physics, climate and finance. It describes the anomalous growth of range and constrains the behavior and predictability of these systems. The Hurst effect is frequently taken to be synonymous with Long-Range Dependence (LRD) and is typically assumed to be produced by a stationary stochastic process which has infinite memory. However, infinite memory appears to be at odds with the Markovian nature of most physical laws while the stationarity assumption lacks robustness. Here we use Lorenz's paradigmatic chaotic model to show that regime behavior can also cause the Hurst effect. By giving an alternative, parsimonious, explanation using nonstationary Markovian dynamics, our results question the common belief that the Hurst effect necessarily implies a stationary infinite memory process. We also demonstrate that our results can explain atmospheric variability without the infinite memory previously thought necessary and are consistent with climate model simulations.
authors.affiliation: Meteorological Institute and Center for Earth System Research and Sustainability (CEN), University of Hamburg, Hamburg, Germany.
authors.forename: Christian L E
authors.initials: CL
authors.lastname: Franzke
authors.affiliation: National Centre for Atmospheric Science and Department of Physics, University of Oxford, Oxford, UK.
authors.forename: Scott M
authors.initials: SM
authors.lastname: Osprey
authors.affiliation: Institute of Atmospheric Sciences and Climate (ISAC-CNR), Torino, Italy.
authors.forename: Paolo
authors.initials: P
authors.lastname: Davini
authors.affiliation: 1] Max-Planck Institute for the Physics of Complex Systems, Dresden, Germany [2] Centre for the Analysis of Time Series, LSE, London, UK [3] MCT, Open University, Milton Keynes, UK [4] CFSA, University of Warwick, Coventry, UK.
authors.forename: Nicholas W
authors.initials: NW
authors.lastname: Watkins