Generating surrogate data for time series with several simultaneously measured variables

1994 ◽  
Vol 73 (7) ◽  
pp. 951-954 ◽  
Author(s):  
Dean Prichard ◽  
James Theiler
Keyword(s):  
Time Series ◽  
Surrogate Data

scholarly journals Nonlinear analysis of magnetospheric data Part I. Geometric characteristics of the AE index time series and comparison with nonlinear surrogate data

1999 ◽  
Vol 6 (1) ◽  
pp. 51-65 ◽  
Author(s):  
G. P. Pavlos ◽  
M. A. Athanasiu ◽  
D. Kugiumtzis ◽  
N. Hatzigeorgiu ◽  
A. G. Rigas ◽  
...  
Keyword(s):  
Time Series ◽  
State Space ◽  
Null Hypothesis ◽  
Surrogate Data ◽  
Statistical Testing ◽  
Geometrical Parameters ◽  
Geometric Characteristics ◽  
Geometrical Characteristics ◽  
Ae Index ◽  
Index Time Series

Abstract. A long AE index time series is used as a crucial magnetospheric quantity in order to study the underlying dynainics. For this purpose we utilize methods of nonlinear and chaotic analysis of time series. Two basic components of this analysis are the reconstruction of the experimental tiine series state space trajectory of the underlying process and the statistical testing of an null hypothesis. The null hypothesis against which the experimental time series are tested is that the observed AE index signal is generated by a linear stochastic signal possibly perturbed by a static nonlinear distortion. As dis ' ' ating statistics we use geometrical characteristics of the reconstructed state space (Part I, which is the work of this paper) and dynamical characteristics (Part II, which is the work a separate paper), and "nonlinear" surrogate data, generated by two different techniques which can mimic the original (AE index) signal. lie null hypothesis is tested for geometrical characteristics which are the dimension of the reconstructed trajectory and some new geometrical parameters introduced in this work for the efficient discrimination between the nonlinear stochastic surrogate data and the AE index. Finally, the estimated geometric characteristics of the magnetospheric AE index present new evidence about the nonlinear and low dimensional character of the underlying magnetospheric dynamics for the AE index.

scholarly journals Chaotic Patterns in Aeroelastic Signals

2009 ◽  
Vol 2009 ◽  
pp. 1-19 ◽  
Author(s):  
F. D. Marques ◽  
R. M. G. Vasconcellos
Keyword(s):  
Time Series ◽  
State Space ◽  
Complex Dynamics ◽  
Chaotic Behavior ◽  
Separated Flow ◽  
Direct Analysis ◽  
Surrogate Data ◽  
The State ◽  
Aeroelastic System ◽  
Value Decomposition

This work presents the analysis of nonlinear aeroelastic time series from wing vibrations due to airflow separation during wind tunnel experiments. Surrogate data method is used to justify the application of nonlinear time series analysis to the aeroelastic system, after rejecting the chance for nonstationarity. The singular value decomposition (SVD) approach is used to reconstruct the state space, reducing noise from the aeroelastic time series. Direct analysis of reconstructed trajectories in the state space and the determination of Poincaré sections have been employed to investigate complex dynamics and chaotic patterns. With the reconstructed state spaces, qualitative analyses may be done, and the attractors evolutions with parametric variation are presented. Overall results reveal complex system dynamics associated with highly separated flow effects together with nonlinear coupling between aeroelastic modes. Bifurcations to the nonlinear aeroelastic system are observed for two investigations, that is, considering oscillations-induced aeroelastic evolutions with varying freestream speed, and aeroelastic evolutions at constant freestream speed and varying oscillations. Finally, Lyapunov exponent calculation is proceeded in order to infer on chaotic behavior. Poincaré mappings also suggest bifurcations and chaos, reinforced by the attainment of maximum positive Lyapunov exponents.

scholarly journals APPLICATION OF CHAOS GAME REPRESENTATION TO NONLINEAR TIME SERIES ANALYSIS

Fractals ◽  
2006 ◽  
Vol 14 (01) ◽  
pp. 27-35 ◽  
Author(s):  
TOMOYA SUZUKI ◽  
TOHRU IKEGUCHI ◽  
MASUO SUZUKI
Keyword(s):  
Time Series ◽  
Real Time ◽  
Dna Sequences ◽  
Surrogate Data ◽  
Nonlinear Time Series Analysis ◽  
Conditional Probabilities ◽  
Fractal Structures ◽  
Chaos Game Representation ◽  
Chaos Game ◽  
Game Representation

Iterative function systems are often used for investigating fractal structures. The method is also referred as Chaos Game Representation (CGR), and is applied for representing characteristic structures of DNA sequences visually. In this paper, we proposed an original way of plotting CGR to easily confirm the property of the temporal evaluation of a time series. We also showed existence of spurious characteristic structures of time series, if we carelessly applied the CGR to real time series. We revealed that the source of spurious identification came from non-uniformity of the frequency histograms of the time series, which is often the case of analyzing real time series. We also showed how to avoid such spurious identification by applying the method of surrogate data and introducing conditional probabilities of the time series.

scholarly journals Quantifying Statistical Interdependence by Message Passing on Graphs—Part I: One-Dimensional Point Processes

2009 ◽  
Vol 21 (8) ◽  
pp. 2152-2202 ◽  
Author(s):  
J. Dauwels ◽  
F. Vialatte ◽  
T. Weber ◽  
A. Cichocki
Keyword(s):  
Time Series ◽  
Message Passing ◽  
Point Processes ◽  
Pairwise Alignment ◽  
Surrogate Data ◽  
Map Estimation ◽  
One Dimensional ◽  
Novel Approach ◽  
Average Similarity ◽  
Stochastic Event

We present a novel approach to quantify the statistical interdependence of two time series, referred to as stochastic event synchrony (SES). The first step is to extract “events” from the two given time series. The next step is to try to align events from one time series with events from the other. The better the alignment, the more similar the two time series are considered to be. More precisely, the similarity is quantified by the following parameters: time delay, variance of the timing jitter, fraction of noncoincident events, and average similarity of the aligned events. The pairwise alignment and SES parameters are determined by statistical inference. In particular, the SES parameters are computed by maximum a posteriori (MAP) estimation, and the pairwise alignment is obtained by applying the max-product algorithm. This letter deals with one-dimensional point processes; the extension to multidimensional point processes is considered in a companion letter in this issue. By analyzing surrogate data, we demonstrate that SES is able to quantify both timing precision and event reliability more robustly than classical measures can. As an illustration, neuronal spike data generated by the Morris-Lecar neuron model are considered.

scholarly journals The comparative study of chaoticity and dynamical complexity of the low-latitude ionosphere, over Nigeria, during quiet and disturbed days

2014 ◽  
Vol 21 (1) ◽  
pp. 127-142 ◽  
Author(s):  
B. O. Ogunsua ◽  
J. A. Laoye ◽  
I. A. Fuwape ◽  
A. B. Rabiu
Keyword(s):  
Time Series ◽  
Lyapunov Exponents ◽  
Correlation Dimension ◽  
Chaotic Behavior ◽  
Surrogate Data ◽  
Tsallis Entropy ◽  
Electron Content ◽  
Total Electron ◽  
Dynamical Complexity ◽  
Definite Pattern

Abstract. The deterministic chaotic behavior and dynamical complexity of the space plasma dynamical system over Nigeria are analyzed in this study and characterized. The study was carried out using GPS (Global Positioning System) TEC (Total Electron Content) time series, measured in the year 2011 at three GPS receiver stations within Nigeria, which lies within the equatorial ionization anomaly region. The TEC time series for the five quietest and five most disturbed days of each month of the year were selected for the study. The nonlinear aspect of the TEC time series was obtained by detrending the data. The detrended TEC time series were subjected to various analyses for phase space reconstruction and to obtain the values of chaotic quantifiers like Lyapunov exponents, correlation dimension and also Tsallis entropy for the measurement of dynamical complexity. The observations made show positive Lyapunov exponents (LE) for both quiet and disturbed days, which indicates chaoticity, and for different days the chaoticity of the ionosphere exhibits no definite pattern for either quiet or disturbed days. However, values of LE were lower for the storm period compared with its nearest relative quiet periods for all the stations. The monthly averages of LE and entropy also show no definite pattern for the month of the year. The values of the correlation dimension computed range from 2.8 to 3.5, with the lowest values recorded at the storm period of October 2011. The surrogate data test shows a significance of difference greater than 2 for all the quantifiers. The entropy values remain relatively close, with slight changes in these values during storm periods. The values of Tsallis entropy show similar variation patterns to those of Lyapunov exponents, with a lot of agreement in their comparison, with all computed values of Lyapunov exponents correlating with values of Tsallis entropy within the range of 0.79 to 0.81. These results show that both quantifiers can be used together as indices in the study of the variation of the dynamical complexity of the ionosphere. The results also show a strong play between determinism and stochasticity. The behavior of the ionosphere during these storm and quiet periods for the seasons of the year are discussed based on the results obtained from the chaotic quantifiers.

scholarly journals Quantifying Statistical Interdependence by Message Passing on Graphs—Part II: Multidimensional Point Processes

2009 ◽  
Vol 21 (8) ◽  
pp. 2203-2268 ◽  
Author(s):  
J. Dauwels ◽  
F. Vialatte ◽  
T. Weber ◽  
T. Musha ◽  
A. Cichocki
Keyword(s):  
Time Series ◽  
Message Passing ◽  
Point Processes ◽  
Graphical Model ◽  
Combinatorial Problem ◽  
Pairwise Alignment ◽  
Surrogate Data ◽  
Multidimensional Case ◽  
Inference Problem ◽  
One Dimensional

Stochastic event synchrony is a technique to quantify the similarity of pairs of signals. First, events are extracted from the two given time series. Next, one tries to align events from one time series with events from the other. The better the alignment, the more similar the two time series are considered to be. In Part I, the companion letter in this issue, one-dimensional events are considered; this letter concerns multidimensional events. Although the basic idea is similar, the extension to multidimensional point processes involves a significantly more difficult combinatorial problem and therefore is nontrivial. Also in the multidimensional case, the problem of jointly computing the pairwise alignment and SES parameters is cast as a statistical inference problem. This problem is solved by coordinate descent, more specifically, by alternating the following two steps: (1) estimate the SES parameters from a given pairwise alignment; (2) with the resulting estimates, refine the pairwise alignment. The SES parameters are computed by maximum a posteriori (MAP) estimation (step 1), in analogy to the one-dimensional case. The pairwise alignment (step 2) can no longer be obtained through dynamic programming, since the state space becomes too large. Instead it is determined by applying the max-product algorithm on a cyclic graphical model. In order to test the robustness and reliability of the SES method, it is first applied to surrogate data. Next, it is applied to detect anomalies in EEG synchrony of mild cognitive impairment (MCI) patients. Numerical results suggest that SES is significantly more sensitive to perturbations in EEG synchrony than a large variety of classical synchrony measures.

Wavelet analysis of scaling properties of gastric electrical activity

2006 ◽  
Vol 101 (5) ◽  
pp. 1425-1431 ◽  
Author(s):  
Bruce J. West ◽  
Artur Maciejewski ◽  
Miroslaw Latka ◽  
Tadeusz Sebzda ◽  
Zbigniew Swierczynski ◽  
...  
Keyword(s):  
Time Series ◽  
Systemic Sclerosis ◽  
Surrogate Data ◽  
Long Term Memory ◽  
Wavelet Coefficients ◽  
Healthy Individuals ◽  
Scaling Properties ◽  
Statistical Fluctuations ◽  
Novel Approach ◽  
Scaling Index

We present a novel approach to the analysis of fluctuations in human myoelectrical gastric activity measured noninvasively from the surface of the abdomen. The time intervals between successive maxima of the wavelet transformed quasi-periodic electrogastrographic waveform define the gastric rate variability (GRV) time series. By using the method of average wavelet coefficients, the statistical fluctuations in the GRV signal in healthy individuals are determined to scale in time. Such scaling was previously found in a variety of physiological phenomena, all of which support the hypothesis that physiological dynamics utilize fractal time series. We determine the scaling index in a cohort of 17 healthy individuals to be 0.80 ± 0.14, which compared with a set of surrogate data is found to be significant at the level P < 0.01. We also determined that the dynamical pattern, so evident in the spectrum of average wavelet coefficients of the GRV time series of healthy individuals, is significantly reduced in a cohort of systemic sclerosis patients having a scaling index 0.64 ± 0.17. These results imply that the long-term memory in GRV time series is significantly reduced from healthy individuals to those with systemic sclerosis. Consequently, this disease degrades the complexity of the underlying gastrointestinal control system and this degradation is manifest in the loss of scaling in the GRV time series.

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