Large noise level estimation

Alexandros Leontitsis, Jenny Pange, Tassos Bountis

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


We generalize a method of noise estimation for chaotic time series due to [Schreiber, 1993] in cases where the noise level is relatively large. The noise estimation is based on the correlation integral, which, for small amounts of noise, is not affected by the attractor's curvature effects. When the noise is large, however, one has to increase the range of the correlation integral and this brings about significant inaccuracies in its evaluation due to both curvature effects and noise. In this Letter, we present a modification of Schreiber's noise level estimation method, which uses a robust error estimator based on L-∞ (rather than the usual L2) norm in the computations. Since L-∞ was proved less sensitive to curvature effects, it gives a more accurate estimation of the noise standard deviation compared with Schreiber's results. Here, we illustrate our approach on the Hénon map corrupted by Gaussian white noise with zero mean, as well as on real data obtained from the Nasdaq Composite time series of daily returns.

Original languageEnglish
Pages (from-to)2309-2313
Number of pages5
JournalInternational Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Issue number8
Publication statusPublished - Aug 2003


  • Chaotic time series
  • Noise estimation

ASJC Scopus subject areas

  • Modelling and Simulation
  • Engineering (miscellaneous)
  • General
  • Applied Mathematics

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