T. Schreiber and A. Schmitz, "Surrogate time series," Physica D, vol. 142, no. 3-4, pp. 346--382, 2000. Home/Search Document Details and Download
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Surrogate-Based Test for Granger Causality - Gautama, Van Hulle (Correct)
....causality, xk should be included as input to the cross prediction system. namely the absence of x y Granger causality, is not known, we adopt a bootstrapping procedure for generating an empirical distribution function (EDF) of # o , given H 0 . To this cause, the surrogate data methodology [4, 5] is commonly used in the field of signal nonlinearity testing. In the absence of y Granger causality, a randomisation of x, such as a random permutation of the time samples which retains the signal distribution but makes the signal random otherwise, should not have an e#ect on the ....
....rank r o # (N s 1) the null hypothesis of the absence of x y Granger causality is rejected. Iterative Amplitude Adjusted Correlation (iAAC) Surrogates The rejection of a null hypothesis in a surrogate data framework needs to be interpreted with due caution, as discussed, e.g. in Ref. [4], since there is no information available regarding what aspect of the null hypothesis is violated. In our particular case of instantaneous x y causality, it is well possible that the time series x shows a high degree of correlation to y and r without instantaneously Granger causing y. The ....
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T. Schreiber and A. Schmitz, "Surrogate Time Series," Physica D, vol. 142, no. 3-4, pp. 346--382, 2000.
A Non-Parametric Test for Detecting the Complex-Valued.. - Gautama, Mandic, Van.. (Correct)
....parameters of which are more mathematically involved to determine than those of linear models. A reliable, statistical test for assessing the complex valued nature of a signal, however, is still lacking. To that cause, we extend the iterative Amplitude Adjusted Fourier Transform (iAAFT) approach [5] toward complex valued signals (Section 2) A null hypothesis of a complex valued linear system underlying the time series under study i utilised. Next, a novel methodology is proposed for characterising (Section 3) and statistically testing (Section 4) the complex valued nature of a time series. ....
....of a certain null hypothesis, H 0 . These are further used for bootstrapping the distribution of the test statistic under the assumption of H 0 . In this section, a surrogate data generation procedure known as the (real valued) iterative Amplitude Adjusted Fourier Transform (iAAFT) method [5] is shortly introduced, after which an extension of this method towards complex valued signals is proposed. 2.1 Real Valued iAAFT Method The iAAFT method generates a surrogate for a real valued (univariate) time series under the null hypothesis that the original time series is generated by a ....
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Schreiber, T., Schmitz, A.: Surrogate time series. Physica D 142 (2000) 346--382
A Differential Entropy Based Method For Determining The .. - Gautama, Mandic, Van.. (Correct)
....) yielding the optimal set of embedding parameters fm opt ; opt g. Notice that the K L entropy estimate (Eq. 1) is not robust with respect to dimensionality. This is compensated for by standardising H(x; m; with respect to an ensemble of socalled surrogates of signal x (for an overview, see [5]) In the simplest case, N s surrogates x s;i i = 1; N s of a signal x are generated by performing a random permutation of the time samples. This way, the signal distribution is unaffected and the serial correlations are randomised (yielding a whitened signal with a signal distribution ....
....parameters which have a preference for opt = 1. Indeed, for = 1, the presence of time correlations implies a higher degree of structure, thus, a lower amount of disorder. To that cause, surrogate data are best generated using the iterative Amplitude Adjusted Fourier Transform (iAAFT)method [5], which retains withinthe surrogates boththe signal distributions and also approximately the autocorrelation structure of the original signal. This way, the serial correlations are present in both the original and the surrogate time series, as desired. The minimum of the plot of the entropy ratio ....
T. Schreiber and A. Schmitz, "Surrogate time series," Physica D, vol. 142, no. 3-4, pp. 346--382, 2000.
A Novel Method for Determining the Nature of Time Series - Gautama, Mandic, Van Hulle (Correct)
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T. Schreiber and A. Schmitz, "Surrogate time series," Physica D, vol. 142, no. 3-4, pp. 346--382, 2000.
Synchronization and Interdependence Measures and Their.. - Kraskov (2004) (Correct)
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T. Schreiber and A. Schmitz. Surrogate time series. Physica D, 142:346, 2000.
The Delay Vector Variance Method for Detecting Determinism and .. - Gautama, al. (Correct)
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Schreiber, T., & Schmitz, A. (2000). Surrogate time series, Physica D, 142, 346--382. 20 Figure Captions
Signal Nonlinearity in fMRI: A Comparison between BOLD and.. - Gautama, Mandic, Van Hulle (Correct)
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T. Schreiber and A. Schmitz, "Surrogate time series," Physica D, vol. 142, no. 3-4, pp. 346--382, 2000.
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