A Nonlinearity Measure Based on Surrogate Data Analysis

2008 ◽  
pp. 93-110 ◽  
Author(s):  
Shoukat M. A. A. Choudhury ◽  
Sirish L. Shah ◽  
Nina F. Thornhill
Keyword(s):  
Data Analysis ◽  
Surrogate Data

Surrogate Data Analysis for Assessing the Significance of the Coherence Function

2004 ◽  
Vol 51 (7) ◽  
pp. 1156-1166 ◽  
Author(s):  
L. Faes ◽  
G.D. Pinna ◽  
A. Porta ◽  
R. Maestri ◽  
G.D. Nollo
Keyword(s):  
Data Analysis ◽  
Coherence Function ◽  
Surrogate Data

Surrogate data analysis of sleep electroencephalograms reveals evidence for nonlinearity

1996 ◽  
Vol 75 (1) ◽  
pp. 85-92 ◽  
Author(s):  
Jürgen Fell ◽  
Joachim Röschke ◽  
Cornelius Schäffner
Keyword(s):  
Data Analysis ◽  
Surrogate Data

Modified generalized multiscale sample entropy and surrogate data analysis for financial time series

2018 ◽  
Vol 92 (3) ◽  
pp. 1335-1350 ◽  
Author(s):  
Yue Wu ◽  
Pengjian Shang ◽  
Yilong Li
Keyword(s):  
Time Series ◽  
Data Analysis ◽  
Financial Time Series ◽  
Surrogate Data ◽  
Sample Entropy ◽  
Financial Time

Nonlinear analysis of EEG signals: Surrogate data analysis

IRBM ◽  
2008 ◽  
Vol 29 (4) ◽  
pp. 239-244 ◽  
Author(s):  
R. Kunhimangalam ◽  
P.K. Joseph ◽  
O.K. Sujith
Keyword(s):  
Data Analysis ◽  
Nonlinear Analysis ◽  
Surrogate Data ◽  
Eeg Signals

Surrogate data analysis of sleep electroencephalograms reveals evidence for nonlinearity

1996 ◽  
Vol 75 (1) ◽  
pp. 85-92 ◽  
Author(s):  
J�rgen Fell ◽  
Joachim R�schke ◽  
Cornelius Sch�ffner
Keyword(s):  
Data Analysis ◽  
Surrogate Data

scholarly journals Scaling properties and symmetrical patterns in the epidemiology of rotavirus infection

2003 ◽  
Vol 358 (1438) ◽  
pp. 1625-1641 ◽  
Author(s):  
Marco V. José ◽  
Ruth F. Bishop
Keyword(s):  
Data Analysis ◽  
Young Children ◽  
Power Law ◽  
Surrogate Data ◽  
Fluctuation Analysis ◽  
Mathematical Methods ◽  
Rotavirus Infection ◽  
Epidemic Dynamics ◽  
Data Analysis Technique ◽  
Analysis Technique

The rich epidemiological database of the incidence of rotavirus, as a cause of severe diarrhoea in young children, coupled with knowledge of the natural history of the infection, can make this virus a paradigm for studies of epidemic dynamics. The cyclic recurrence of childhood rotavirus epidemics in unvaccinated populations provides one of the best documented phenomena in population dynamics. This paper makes use of epidemiological data on rotavirus infection in young children admitted to hospital in Melbourne, Australia from 1977 to 2000. Several mathematical methods were used to characterize the overall dynamics of rotavirus infections as a whole and individually as serotypes G1, G2, G3, G4 and G9. These mathematical methods are as follows: seasonal autoregressive integrated moving-average (SARIMA) models, power spectral density (PSD), higher-order spectral analysis (HOSA) (bispectrum estimation and quadratic phase coupling (QPC)), detrended fluctuation analysis (DFA), wavelet analysis (WA) and a surrogate data analysis technique. Each of these techniques revealed different dynamic aspects of rotavirus epidemiology. In particular, we confirm the existence of an annual, biannual and a quinquennial period but additionally we found other embedded cycles (e.g. ca . 3 years). There seems to be an overall unique geometric and dynamic structure of the data despite the apparent changes in the dynamics of the last years. The inherent dynamics seems to be conserved regardless of the emergence of new serotypes, the re-emergence of old serotypes or the transient disappearance of a particular serotype. More importantly, the dynamics of all serotypes is multiple synchronized so that they behave as a single entity at the epidemic level. Overall, the whole dynamics follow a scale-free power-law fractal scaling behaviour. We found that there are three different scaling regions in the time-series, suggesting that processes influencing the epidemic dynamics of rotavirus over less than 12 months differ from those that operate between 1 and ca . 3 years, as well as those between 3 and ca . 5 years. To discard the possibility that the observed patterns could be due to artefacts, we applied a surrogate data analysis technique which enabled us to discern if only random components or linear features of the incidence of rotavirus contribute to its dynamics. The global dynamics of the epidemic is portrayed by wavelet-based incidence analysis. The resulting wavelet transform of the incidence of rotavirus crisply reveals a repeating pattern over time that looks similar on many scales (a property called self-similarity). Both the self-similar behaviour and the absence of a single characteristic scale of the power-law fractal-like scaling of the incidence of rotavirus infection imply that there is not a universal inherently more virulent serotype to which severe gastroenteritis can uniquely be ascribed.

Modified generalized sample entropy and surrogate data analysis for stock markets

2016 ◽  
Vol 35 ◽  
pp. 17-24 ◽  
Author(s):  
Mengjia Xu ◽  
Pengjian Shang ◽  
Jingjing Huang
Keyword(s):  
Data Analysis ◽  
Stock Markets ◽  
Surrogate Data ◽  
Sample Entropy

scholarly journals Reliable Estimation of Minimum Embedding Dimension Through Statistical Analysis of Nearest Neighbors

2017 ◽  
Vol 12 (5) ◽  
Author(s):  
David Chelidze
Keyword(s):  
Time Series ◽  
Data Analysis ◽  
Nearest Neighbor ◽  
Nearest Neighbors ◽  
Surrogate Data ◽  
Original Method ◽  
Random Time ◽  
Embedding Dimension ◽  
False Nearest Neighbors ◽  
Coordinate Embedding

False nearest neighbors (FNN) is one of the essential methods used in estimating the minimally sufficient embedding dimension in delay-coordinate embedding of deterministic time series. Its use for stochastic and noisy deterministic time series is problematic and erroneously indicates a finite embedding dimension. Various modifications to the original method have been proposed to mitigate this problem, but those are still not reliable for noisy time series. Here, nearest-neighbor statistics are studied for uncorrelated random time series and contrasted with the corresponding deterministic and stochastic statistics. New composite FNN metrics are constructed and their performance is evaluated for deterministic, correlates stochastic, and white random time series. In addition, noise-contaminated deterministic data analysis shows that these composite FNN metrics are robust to noise. All FNN results are also contrasted with surrogate data analysis to show their robustness. The new metrics clearly identify random time series as not having a finite embedding dimension and provide information about the deterministic part of correlated stochastic processes. These metrics can also be used to differentiate between chaotic and random time series.

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