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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.

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Author:Andrey G. CherstvyORCiD, Deepak Vinod, Erez Aghion, Aleksei V. ChechkinORCiDGND, Ralf MetzlerORCiDGND
Parent Title (English):New journal of physics
Place of publication:London
Document Type:Article
Date of first Publication:2017/06/30
Year of Completion:2017
Publishing Institution:Universität Potsdam
Release Date:2017/09/01
Tag:diffusion; financial time series; geometric Brownian motion; time averaging
First Page:1
Last Page:11
Funder:Universität Potsdam, Publikationsfonds
Grant Number:PA 2017_27
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik
Peer Review:Referiert
Grantor:Publikationsfonds der Universität Potsdam
Publication Way:Open Access
Licence (English):License LogoCreative Commons - Attribution 3.0 Unported
Notes extern:Zweitveröffentlichung in der Schriftenreihe Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe ; 347