Time averaging, ageing and delay analysis of financial time series

Andrey G. Cherstvy, Deepak Vinod, Erez Aghion, Aleksei V. Chechkin, Ralf Metzler

Research output: Contribution to journalArticlepeer-review

27 Scopus citations


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.

Original languageEnglish
Article number063045
JournalNew Journal of Physics
Issue number6
StatePublished - Jun 2017

Bibliographical note

Publisher Copyright:
© 2017 IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.


  • diffusion
  • financial time series
  • geometric Brownian motion
  • time averaging


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