scholarly journals Streamflow dynamics at the Puget Sound, Washington: application of a surrogate data method

2005 ◽  
Vol 12 (4) ◽  
pp. 461-469 ◽  
Author(s):  
N. She ◽  
D. Basketfield
Keyword(s):  
Time Series ◽  
Null Hypothesis ◽  
Puget Sound ◽  
Original Data ◽  
Surrogate Data ◽  
Linear Process ◽  
Central Basin ◽  
Daily Streamflow ◽  
Streamflow Data ◽  
Dynamic Nonlinearity

Abstract. Recent progress in nonlinear dynamic theory has inspired hydrologists to apply innovative nonlinear time series techniques to the analysis of streamflow data. However, regardless of the method employed to analyze streamflow data, the first step should be the identification of underlying dynamics using one or more methods that could distinguish between linear and nonlinear, deterministic and stochastic processes from data itself. In recent years a statistically rigorous framework to test whether or not the examined time series is generated by a Gaussian (linear) process undergoing a possibly nonlinear static transform is provided by the method of surrogate data. The surrogate data, generated to represent the null hypothesis, are compared to the original data under a nonlinear discriminating statistic in order to reject or approve the null hypothesis. In recognition of this tendency, the method of "surrogate data" is applied herein to determine the underlying linear stochastic or nonlinear deterministic nature of daily streamflow data observed from the central basin of Puget Sound, and as applicable, distinguish between the static or dynamic nonlinearity of the data in question.

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.

ON THE RELIABILITY OF THE SURROGATE DATA TEST FOR NONLINEARITY IN THE ANALYSIS OF NOISY TIME SERIES

2001 ◽  
Vol 11 (07) ◽  
pp. 1881-1896 ◽  
Author(s):  
D. KUGIUMTZIS
Keyword(s):  
Time Series ◽  
Null Hypothesis ◽  
Volterra Series ◽  
Simulated Data ◽  
Real Data ◽  
Surrogate Data ◽  
Largest Lyapunov Exponent ◽  
Real World Data ◽  
Original Time ◽  
False Nearest Neighbors

In the analysis of real world data, the surrogate data test is often performed in order to investigate nonlinearity in the data. The null hypothesis of the test is that the original time series is generated from a linear stochastic process possibly undergoing a nonlinear static transform. We argue against reported rejection of the null hypothesis and claims of evidence of nonlinearity based on a single nonlinear statistic. In particular, two schemes for the generation of surrogate data are examined, the amplitude adjusted Fourier transform (AAFT) and the iterated AAFT (IAFFT) and many nonlinear discriminating statistics are used for testing, i.e. the fit with the Volterra series of polynomials and the fit with local average mappings, the mutual information, the correlation dimension, the false nearest neighbors, the largest Lyapunov exponent and simple nonlinear averages (the three point autocorrelation and the time reversal asymmetry). The results on simulated data and real data (EEG and exchange rates) suggest that the test depends on the method and its parameters, the algorithm generating the surrogate data and the observational data of the examined process.

SURROGATE DATA PATHOLOGIES AND THE FALSE-POSITIVE REJECTION OF THE NULL HYPOTHESIS

2001 ◽  
Vol 11 (04) ◽  
pp. 983-997 ◽  
Author(s):  
P. E. RAPP ◽  
C. J. CELLUCCI ◽  
T. A. A. WATANABE ◽  
A. M. ALBANO ◽  
T. I. SCHMAH
Keyword(s):  
Time Series ◽  
Fourier Transform ◽  
False Positive ◽  
Null Hypothesis ◽  
Random Phase ◽  
Surrogate Data ◽  
Random Numbers ◽  
Nonlinear Structure ◽  
Numerical Errors ◽  
Comparison Test

It is shown that inappropriately constructed random phase surrogates can give false-positive rejections of the surrogate null hypothesis. Specifically, the procedure erroneously indicated the presence of deterministic, nonlinear structure in a time series that was constructed by linearly filtering normally distributed random numbers. It is shown that the erroneous identification was due to numerical errors in the estimation of the signal's Fourier transform. In the example examined here, the introduction of data windowing into the algorithm eliminated the false-positive rejection of the null hypothesis. Additional guidelines for the use of surrogates are considered, and the results of a comparison test of random phase surrogates, Gaussian scaled surrogates and iterative surrogates are presented.

Data Preprocessing

2018 ◽  
Author(s):  
Ray Huffaker ◽  
Marco Bittelli ◽  
Rodolfo Rosa
Keyword(s):  
Stochastic Process ◽  
Time Series ◽  
Signal Processing ◽  
Real World ◽  
Null Hypothesis ◽  
Time Series Data ◽  
Nonlinear Behavior ◽  
Surrogate Data ◽  
Series Data ◽  
Linear Behavior

Successful reconstruction of a shadow attractor provides preliminary empirical evidence that a signal isolated from observed time series data may be generated by deterministic dynamics. However, because we cannot reasonably expect signal processing to purge the signal of all noise in practice, and because noisy linear behavior can be visually indistinguishable from nonlinear behavior, the possibility remains that noticeable regularity detected in a shadow attractor may be fortuitously reconstructed from data generated by a linear-stochastic process. This chapter investigates how we can test this null hypothesis using surrogate data testing. The combination of a noticeably regular shadow attractor, along with strong statistical rejection of fortuitous regularity, increases the probability that observed data are generated by deterministic real-world dynamics.

TESTING FOR NONLINEARITY IN SHANGHAI STOCK MARKET

2004 ◽  
Vol 18 (17n19) ◽  
pp. 2720-2724 ◽  
Author(s):  
HAIYAN WANG ◽  
LONGKUN TANG
Keyword(s):  
Time Series ◽  
Stock Market ◽  
Null Hypothesis ◽  
Quantitative Method ◽  
Multivariate Time Series ◽  
Surrogate Data ◽  
Significance Test ◽  
Test Statistic ◽  
Gaussian Random Process ◽  
Linear And Nonlinear

In this paper, we apply IAAFT to generate surrogate time series of measured multivariate time series. A quantitative method to detect nonlinearity in multivariate time series is proposed using the generalized redundancy and linear redundancy as the significance test statistic. The null hypothesis of a multivariate linear Gaussian random process is tested using the multivariate surrogate data. The validity of this method is demonstrated using two types models (linear and nonlinear) and applied to Shanghai stock market.

scholarly journals The role of climatic and terrain attributes in estimating baseflow recession in tropical catchments

2010 ◽  
Vol 14 (11) ◽  
pp. 2193-2205 ◽  
Author(s):  
J. L. Peña-Arancibia ◽  
A. I. J. M. van Dijk ◽  
M. Mulligan ◽  
L. A. Bruijnzeel
Keyword(s):  
Potential Evapotranspiration ◽  
Aridity Index ◽  
Global Scale ◽  
Tree Cover ◽  
Annual Rainfall ◽  
Ungauged Catchments ◽  
Ongoing Research ◽  
Daily Streamflow ◽  
Terrain Attributes ◽  
Streamflow Data

Abstract. The understanding of low flows in rivers is paramount more than ever as demand for water increases on a global scale. At the same time, limited streamflow data to investigate this phenomenon, particularly in the tropics, makes the provision of accurate estimations in ungauged areas an ongoing research need. This paper analysed the potential of climatic and terrain attributes of 167 tropical and sub-tropical unregulated catchments to predict baseflow recession rates. Daily streamflow data (m3 s–1) from the Global River Discharge Center (GRDC) and a linear reservoir model were used to obtain baseflow recession coefficients (kbf) for these catchments. Climatic attributes included annual and seasonal indicators of rainfall and potential evapotranspiration. Terrain attributes included indicators of catchment shape, morphology, land cover, soils and geology. Stepwise regression was used to identify the best predictors for baseflow recession coefficients. Mean annual rainfall (MAR) and aridity index (AI) were found to explain 49% of the spatial variation of kbf. The rest of climatic indices and the terrain indices average catchment slope (SLO) and tree cover were also good predictors, but co-correlated with MAR. Catchment elongation (CE), a measure of catchment shape, was also found to be statistically significant, although weakly correlated. An analysis of clusters of catchments of smaller size, showed that in these areas, presumably with some similarity of soils and geology due to proximity, residuals of the regression could be explained by SLO and CE. The approach used provides a potential alternative for kbf parameterisation in ungauged catchments.

scholarly journals Nonlinear Dynamic Identification of Beams Resting on Nonlinear Viscoelastic Foundations Based on the Time-Delayed Transfer Entropy and Improved Surrogate Data Algorithm

2018 ◽  
Vol 2018 ◽  
pp. 1-14 ◽  
Author(s):  
Guohua Liu ◽  
Changpeng Ye ◽  
Xu Liang ◽  
Zhongkai Xie ◽  
Ziyuan Yu
Keyword(s):  
Lateral Displacement ◽  
Time History ◽  
Original Data ◽  
Surrogate Data ◽  
Transfer Entropy ◽  
Dynamic Identification ◽  
Concentrated Load ◽  
Nonlinear Foundation ◽  
Young’S Moduli ◽  
The Galerkin Method

In this work, the transfer entropy and surrogate data algorithm were introduced to identify the nonlinearity level of the system by using a numerical solution of nonlinear response of beams. A homogeneous Euler-Bernoulli beam was subjected to a time-varying concentrated load and resting on a nonlinear foundation. The Galerkin method was applied to discretize the dimensionless differential governing equation of the forced vibration, and then the fourth-order Runge-Kutta method was used to obtain the time-history response of the lateral displacement. In order to simulate different nonlinearity levels, different ratios between nonlinear parameters and linear parameters of foundation, as well as different Young’s moduli, were used. A nonlinearity index was proposed. In the case of different nonlinearity levels, the nonlinearity index was used to analyze the difference between the transfer entropy calculated from the original data and the transfer entropy calculated from the surrogate data. By comparing and analyzing the nonlinearity index values under different ratios, it was found that the nonlinearity index values generally increased with the increase of the ratio and the sum of nonlinearity index values had a positive correlation with the ratio. By comparing the nonlinearity index values of the transfer entropy results of beams with different Young's moduli, it was found that the sum of the nonlinearity index values generally decreased with the increase of Young's modulus. The numerical results demonstrate that the present approach could effectively quantify the nonlinearity in the response of a beam resting on a nonlinear foundation.

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