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
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
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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