57765
2022
2022
eng
033055-1
033055-16
16
3
4
article
American Physical Society
College Park, MD
1
2022-07-18
2022-07-18
--
Unravelling the origins of anomalous diffusion
Anomalous diffusion or, more generally, anomalous transport, with nonlinear dependence of the mean-squared displacement on the measurement time, is ubiquitous in nature. It has been observed in processes ranging from microscopic movement of molecules to macroscopic, large-scale paths of migrating birds. Using data from multiple empirical systems, spanning 12 orders of magnitude in length and 8 orders of magnitude in time, we employ a method to detect the individual underlying origins of anomalous diffusion and transport in the data. This method decomposes anomalous transport into three primary effects: long-range correlations (“Joseph effect”), fat-tailed probability density of increments (“Noah effect”), and nonstationarity (“Moses effect”). We show that such a decomposition of real-life data allows us to infer nontrivial behavioral predictions and to resolve open questions in the fields of single-particle tracking in living cells and movement ecology.
Physical Review Research
from molecules to migrating storks
10.1103/PhysRevResearch.4.033055
2643-1564
3004165-X
Universität Potsdam
PA 2022_083
2402,10
Metzler, Ralf
<a href="https://doi.org/10.25932/publishup-57764">Zweitveröffentlichung in der Schriftenreihe Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe ; 1303</a>
CC-BY - Namensnennung 4.0 International
Ohad Vilk
Erez Aghion
Tal Avgar
Carsten Beta
Oliver Nagel
Adal Sabri
Raphael Sarfati
Daniel K. Schwartz
Matthias Weiß
Diego Krapf
Ran Nathan
Ralf Metzler
Michael Assaf
Physik
Institut für Physik und Astronomie
Referiert
Publikationsfonds der Universität Potsdam
Gold Open-Access
40053
2017
2017
eng
1
11
11
19
article
IOP
London
1
--
2017-06-30
--
Time averaging, ageing and delay analysis of financial time series
We introduce three strategies for the analysis of financial time series based on time averaged observables. These comprise the time averaged mean squared displacement (MSD) as well as the ageing and delay time methods for varying fractions of the financial time series. We explore these concepts via statistical analysis of historic time series for several Dow Jones Industrial indices for the period from the 1960s to 2015. Remarkably, we discover a simple universal law for the delay time averaged MSD. The observed features of the financial time series dynamics agree well with our analytical results for the time averaged measurables for geometric Brownian motion, underlying the famed Black–Scholes–Merton model. The concepts we promote here are shown to be useful for financial data analysis and enable one to unveil new universal features of stock market dynamics.
New journal of physics
10.1088/1367-2630/aa7199
1367-2630
Universität Potsdam, Publikationsfonds
PA 2017_27
1299.48
online registration
063045
<a href="http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-400541">Zweitveröffentlichung in der Schriftenreihe Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe ; 347</a>
Andrey G. Cherstvy
Deepak Vinod
Erez Aghion
Aleksei V. Chechkin
Ralf Metzler
eng
uncontrolled
time averaging
eng
uncontrolled
diffusion
eng
uncontrolled
geometric Brownian motion
eng
uncontrolled
financial time series
Physik
Institut für Physik und Astronomie
Referiert
Publikationsfonds der Universität Potsdam
Open Access
Universität Potsdam
40054
2017
2017
eng
11
postprint
1
--
2017-09-01
--
Time averaging, ageing and delay analysis of financial time series
We introduce three strategies for the analysis of financial time series based on time averaged observables. These comprise the time averaged mean squared displacement (MSD) as well as the ageing and delay time methods for varying fractions of the financial time series. We explore these concepts via statistical analysis of historic time series for several Dow Jones Industrial indices for the period from the 1960s to 2015. Remarkably, we discover a simple universal law for the delay time averaged MSD. The observed features of the financial time series dynamics agree well with our analytical results for the time averaged measurables for geometric Brownian motion, underlying the famed Black–Scholes–Merton model. The concepts we promote here are shown to be useful for financial data analysis and enable one to unveil new universal features of stock market dynamics.
urn:nbn:de:kobv:517-opus4-400541
online registration
New journal of physics 19 (2017) 063045. - DOI: 10.1088/1367-2630/aa7199
<a href="http://publishup.uni-potsdam.de/opus4-ubp/frontdoor/index/index/docId/40053">Bibliographieeintrag der Originalveröffentlichung/Quelle</a>
Keine öffentliche Lizenz: Unter Urheberrechtsschutz
Andrey G. Cherstvy
Deepak Vinod
Erez Aghion
Aleksei V. Chechkin
Ralf Metzler
Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
347
eng
uncontrolled
diffusion
eng
uncontrolled
financial time series
eng
uncontrolled
geometric Brownian motion
eng
uncontrolled
time averaging
Physik
open_access
Institut für Physik und Astronomie
Referiert
Open Access
Universität Potsdam
https://publishup.uni-potsdam.de/files/40054/pmn347_online.pdf
46566
2017
2017
eng
135
147
11
19
article
IOP Publ. Ltd.
Bristol
1
--
--
--
Time averaging, ageing and delay analysis of financial time series
We introduce three strategies for the analysis of financial time series based on time averaged observables. These comprise the time averaged mean squared displacement (MSD) as well as the ageing and delay time methods for varying fractions of the financial time series. We explore these concepts via statistical analysis of historic time series for several Dow Jones Industrial indices for the period from the 1960s to 2015. Remarkably, we discover a simple universal law for the delay time averaged MSD. The observed features of the financial time series dynamics agree well with our analytical results for the time averaged measurables for geometric Brownian motion, underlying the famed Black-Scholes-Merton model. The concepts we promote here are shown to be useful for financial data analysis and enable one to unveil new universal features of stock market dynamics.
New journal of physics : the open-access journal for physics
10.1088/1367-2630/aa7199
1367-2630
wos:2017
063045
WOS:000404761900008
Metzler, R (reprint author), Univ Potsdam, Inst Phys & Astron, D-14476 Golm, Germany., a.cherstvy@gmail.com; rmetzler@uni-potsdam.de
DAAD fellowship; KoUP grant of the University of Potsdam; MINERVA Short-Term Research Grant; Deutsche Forschungsgemeinschaft [ME 1535/6-1]; Potsdam University
importub
2020-04-20T02:32:01+00:00
filename=package.tar
fa7857b644526f0efe9dbb30f824a35f
Andrey G. Cherstvy
Deepak Vinod
Erez Aghion
Aleksei V. Chechkin
Ralf Metzler
eng
uncontrolled
time averaging
eng
uncontrolled
diffusion
eng
uncontrolled
geometric Brownian motion
eng
uncontrolled
financial time series
Institut für Physik und Astronomie
Referiert
Import
57764
2022
2022
eng
16
1303
postprint
1
2022-07-18
2022-07-18
--
Unravelling the origins of anomalous diffusion
Anomalous diffusion or, more generally, anomalous transport, with nonlinear dependence of the mean-squared displacement on the measurement time, is ubiquitous in nature. It has been observed in processes ranging from microscopic movement of molecules to macroscopic, large-scale paths of migrating birds. Using data from multiple empirical systems, spanning 12 orders of magnitude in length and 8 orders of magnitude in time, we employ a method to detect the individual underlying origins of anomalous diffusion and transport in the data. This method decomposes anomalous transport into three primary effects: long-range correlations (“Joseph effect”), fat-tailed probability density of increments (“Noah effect”), and nonstationarity (“Moses effect”). We show that such a decomposition of real-life data allows us to infer nontrivial behavioral predictions and to resolve open questions in the fields of single-particle tracking in living cells and movement ecology.
Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
from molecules to migrating storks
10.25932/publishup-57764
urn:nbn:de:kobv:517-opus4-577643
1866-8372
Version of record
<a href="http://publishup.uni-potsdam.de/57765">Bibliographieeintrag der Originalveröffentlichung/Quelle</a>
CC-BY - Namensnennung 4.0 International
Ohad Vilk
Erez Aghion
Tal Avgar
Carsten Beta
Oliver Nagel
Adal Sabri
Raphael Sarfati
Daniel K. Schwartz
Matthias Weiß
Diego Krapf
Ran Nathan
Ralf Metzler
Michael Assaf
Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
1303
Physik
open_access
Institut für Physik und Astronomie
Referiert
Green Open-Access
Universität Potsdam
https://publishup.uni-potsdam.de/files/57764/pmnr1303.pdf
62540
2021
2021
eng
11
6
103
article
American Physical Society
College Park
1
2021-06-15
2021-06-15
--
Scaled geometric Brownian motion features sub- or superexponential ensemble-averaged, but linear time-averaged mean-squared displacements
Various mathematical Black-Scholes-Merton-like models of option pricing employ the paradigmatic stochastic process of geometric Brownian motion (GBM). The innate property of such models and of real stock-market prices is the roughly exponential growth of prices with time [on average, in crisis-free times]. We here explore the ensemble- and time averages of a multiplicative-noise stochastic process with power-law-like time-dependent volatility, sigma(t) similar to t(alpha), named scaled GBM (SGBM). For SGBM, the mean-squared displacement (MSD) computed for an ensemble of statistically equivalent trajectories can grow faster than exponentially in time, while the time-averaged MSD (TAMSD)-based on a sliding-window averaging along a single trajectory-is always linear at short lag times Delta. The proportionality factor between these the two averages of the time series is Delta/T at short lag times, where T is the trajectory length, similarly to GBM. This discrepancy of the scaling relations and pronounced nonequivalence of the MSD and TAMSD at Delta/T << 1 is a manifestation of weak ergodicity breaking for standard GBM and for SGBM with s (t)-modulation, the main focus of our analysis. The analytical predictions for the MSD and mean TAMSD for SGBM are in quantitative agreement with the results of stochastic computer simulations.
Physical review : E, Statistical, nonlinear and soft matter physics
10.1103/PhysRevE.103.062127
34271619
2470-0045
2470-0053
outputup:dataSource:WoS:2021
062127
WOS:000661862700003
Cherstvy, AG (corresponding author), Univ Potsdam, Inst Phys & Astron, D-14476 Potsdam, Germany., a.cherstvy@gmail.com; ugdeepakv@gmail.com; erezagh5@gmail.com; <br /> igor.sokolov@physik.hu-berlin.de; rmetzler@uni-potsdam.de
Humboldt University of Berlin; Deutsche Forschungsgemeinschaft (DFG)German Research Foundation (DFG) [ME 1535/7-1, ME 1535/12-1]; Foundation for Polish Science (Fundacja na rzecz Nauki Polskiej) within an Alexander von Humboldt Polish Honorary Research Scholarship
2024-02-06T10:06:19+00:00
sword
importub
filename=package.tar
968d4ad06e3b6155ea69b376497f7a19
1472725-0
2844562-4
1144458-7
false
true
Keine öffentliche Lizenz: Unter Urheberrechtsschutz
Andrey G. Cherstvy
Deepak Vinod
Erez Aghion
Igor M. Sokolov
Ralf Metzler
Physik
Institut für Physik und Astronomie
Referiert
Import
62852
2022
2022
eng
22
27
55
article
IOP Publ. Ltd.
Bristol
1
2022-06-13
2022-06-13
--
Decomposing the effect of anomalous diffusion enables direct calculation of the Hurst exponent and model classification for single random paths
Recently, a large number of research teams from around the world collaborated in the so-called 'anomalous diffusion challenge'. Its aim: to develop and compare new techniques for inferring stochastic models from given unknown time series, and estimate the anomalous diffusion exponent in data. We use various numerical methods to directly obtain this exponent using the path increments, and develop a questionnaire for model selection based on feature analysis of a set of known stochastic processes given as candidates. Here, we present the theoretical background of the automated algorithm which we put for these tasks in the diffusion challenge, as a counter to other pure data-driven approaches.
Journal of physics / Institute of Physics. A, Mathematical, nuclear and general
10.1088/1751-8121/ac72d4
1751-8113
1751-8121
outputup:dataSource:WoS:2022
274001
WOS:000811481200001
Aghion, E (corresponding author), Max Planck Inst Phys Komplexer Syst, D-01187 Dresden, Germany.; Aghion, E (corresponding author), Univ Massachusetts, Dept Phys, Boston, MA 02125 USA.; Aghion, E (corresponding author), Univ Massachusetts, Dept Chem, Boston, MA 02125 USA., philipp.meyer@uni-potsdam.de; erezagh5@gmail.com
Aghion, Erez
2024-03-01T13:38:47+00:00
sword
importub
filename=package.tar
c835655f285e0a47d3162a6bab146d73
false
true
Philipp Meyer
Erez Aghion
Holger Kantz
eng
uncontrolled
time-series analysis
eng
uncontrolled
decomposing anomalous diffusion
eng
uncontrolled
anomalous
eng
uncontrolled
diffusion exponent
eng
uncontrolled
process inference
Physik
Institut für Physik und Astronomie
Referiert
Import