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 language | English |
|---|---|
| Pages (from-to) | 2309-2313 |
| Number of pages | 5 |
| Journal | International Journal of Bifurcation and Chaos in Applied Sciences and Engineering |
| Volume | 13 |
| Issue number | 8 |
| DOIs | |
| Publication status | Published - Aug 2003 |
| Externally published | Yes |
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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 journal › Article
}
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 -