Large noise level estimation

Alexandros Leontitsis, Jenny Pange, Tassos Bountis

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

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
Volume13
Issue number8
DOIs
Publication statusPublished - Aug 2003
Externally publishedYes

Fingerprint

Correlation Integral
Noise Estimation
Curvature
Time series
Chaotic Time Series
Robust Estimators
Error Estimator
Gaussian White Noise
Standard deviation
Attractor
White noise
Composite
Norm
Generalise
Evaluation
Zero
Range of data
Composite materials

Keywords

  • Chaotic time series
  • Noise estimation

ASJC Scopus subject areas

  • General
  • Applied Mathematics

Cite this

Large noise level estimation. / Leontitsis, Alexandros; Pange, Jenny; Bountis, Tassos.

In: International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, Vol. 13, No. 8, 08.2003, p. 2309-2313.

Research output: Contribution to journalArticle

Leontitsis, Alexandros ; Pange, Jenny ; Bountis, Tassos. / Large noise level estimation. In: International Journal of Bifurcation and Chaos in Applied Sciences and Engineering. 2003 ; Vol. 13, No. 8. pp. 2309-2313.
@article{259500687f72444f98384b4768cbd15c,
title = "Large noise level estimation",
abstract = "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 H{\'e}non 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.",
keywords = "Chaotic time series, Noise estimation",
author = "Alexandros Leontitsis and Jenny Pange and Tassos Bountis",
year = "2003",
month = "8",
doi = "10.1142/S0218127403007965",
language = "English",
volume = "13",
pages = "2309--2313",
journal = "International Journal of Bifurcation and Chaos in Applied Sciences and Engineering",
issn = "0218-1274",
publisher = "World Scientific Publishing Co. Pte Ltd",
number = "8",

}

TY - JOUR

T1 - Large noise level estimation

AU - Leontitsis, Alexandros

AU - Pange, Jenny

AU - Bountis, Tassos

PY - 2003/8

Y1 - 2003/8

N2 - 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.

AB - 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.

KW - Chaotic time series

KW - Noise estimation

UR - http://www.scopus.com/inward/record.url?scp=0242582489&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0242582489&partnerID=8YFLogxK

U2 - 10.1142/S0218127403007965

DO - 10.1142/S0218127403007965

M3 - Article

AN - SCOPUS:0242582489

VL - 13

SP - 2309

EP - 2313

JO - International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

JF - International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

SN - 0218-1274

IS - 8

ER -