Surrogate-based hypothesis test without surrogates

Marco Thiel, M Carmen Romano, U. Schwarz, Juergen Kurths, J. Timmer

Research output: Contribution to journalArticle

Abstract

Fourier surrogate data are artificially generated time series, that - based on a resampling scheme - share the linear properties with an observed time series. In this paper we study a statistical surrogate hypothesis test to detect deviations from a linear Gaussian process with respect to asymmetry in time (Q-statistic). We apply this test to a Fourier representable function and obtain a representation of the asymmetry in time of the sample data, a characteristic for nonlinear processes, and the significance in terms of the Fourier coefficients. The main outcome is that we calculate the expected value of the mean and the standard deviation of the asymmetries of the surrogate data analytically and hence, no surrogates have to be generated. To illustrate the results we apply our method to the saw tooth function, the Lorenz system and to measured X-ray data of Cygnus X-1.
Original languageEnglish
Pages (from-to)2107-2114
Number of pages8
JournalInternational Journal of Bifurcation and Chaos
Volume14
Issue number6
DOIs
Publication statusPublished - Jun 2004

Fingerprint

Hypothesis Test
Surrogate Data
Asymmetry
Time series
Saw tooth
Linear Process
Lorenz System
Nonlinear Process
Statistics
Resampling
Fourier coefficients
Expected Value
Gaussian Process
X rays
Standard deviation
Statistic
Deviation
Calculate

Keywords

  • Fourier surrogates
  • nonlinear time series analysis
  • time-series
  • cygnus X-1
  • nonlinearity
  • variability

Cite this

Surrogate-based hypothesis test without surrogates. / Thiel, Marco; Romano, M Carmen; Schwarz, U.; Kurths, Juergen; Timmer, J.

In: International Journal of Bifurcation and Chaos, Vol. 14, No. 6, 06.2004, p. 2107-2114.

Research output: Contribution to journalArticle

Thiel, Marco ; Romano, M Carmen ; Schwarz, U. ; Kurths, Juergen ; Timmer, J. / Surrogate-based hypothesis test without surrogates. In: International Journal of Bifurcation and Chaos. 2004 ; Vol. 14, No. 6. pp. 2107-2114.
@article{f08d5ea843dc4a24a4194edf33974ce5,
title = "Surrogate-based hypothesis test without surrogates",
abstract = "Fourier surrogate data are artificially generated time series, that - based on a resampling scheme - share the linear properties with an observed time series. In this paper we study a statistical surrogate hypothesis test to detect deviations from a linear Gaussian process with respect to asymmetry in time (Q-statistic). We apply this test to a Fourier representable function and obtain a representation of the asymmetry in time of the sample data, a characteristic for nonlinear processes, and the significance in terms of the Fourier coefficients. The main outcome is that we calculate the expected value of the mean and the standard deviation of the asymmetries of the surrogate data analytically and hence, no surrogates have to be generated. To illustrate the results we apply our method to the saw tooth function, the Lorenz system and to measured X-ray data of Cygnus X-1.",
keywords = "Fourier surrogates, nonlinear time series analysis, time-series, cygnus X-1, nonlinearity, variability",
author = "Marco Thiel and Romano, {M Carmen} and U. Schwarz and Juergen Kurths and J. Timmer",
year = "2004",
month = "6",
doi = "10.1142/S0218127404010527",
language = "English",
volume = "14",
pages = "2107--2114",
journal = "International Journal of Bifurcation and Chaos",
issn = "0218-1274",
publisher = "WORLD SCIENTIFIC PUBL CO PTE LTD",
number = "6",

}

TY - JOUR

T1 - Surrogate-based hypothesis test without surrogates

AU - Thiel, Marco

AU - Romano, M Carmen

AU - Schwarz, U.

AU - Kurths, Juergen

AU - Timmer, J.

PY - 2004/6

Y1 - 2004/6

N2 - Fourier surrogate data are artificially generated time series, that - based on a resampling scheme - share the linear properties with an observed time series. In this paper we study a statistical surrogate hypothesis test to detect deviations from a linear Gaussian process with respect to asymmetry in time (Q-statistic). We apply this test to a Fourier representable function and obtain a representation of the asymmetry in time of the sample data, a characteristic for nonlinear processes, and the significance in terms of the Fourier coefficients. The main outcome is that we calculate the expected value of the mean and the standard deviation of the asymmetries of the surrogate data analytically and hence, no surrogates have to be generated. To illustrate the results we apply our method to the saw tooth function, the Lorenz system and to measured X-ray data of Cygnus X-1.

AB - Fourier surrogate data are artificially generated time series, that - based on a resampling scheme - share the linear properties with an observed time series. In this paper we study a statistical surrogate hypothesis test to detect deviations from a linear Gaussian process with respect to asymmetry in time (Q-statistic). We apply this test to a Fourier representable function and obtain a representation of the asymmetry in time of the sample data, a characteristic for nonlinear processes, and the significance in terms of the Fourier coefficients. The main outcome is that we calculate the expected value of the mean and the standard deviation of the asymmetries of the surrogate data analytically and hence, no surrogates have to be generated. To illustrate the results we apply our method to the saw tooth function, the Lorenz system and to measured X-ray data of Cygnus X-1.

KW - Fourier surrogates

KW - nonlinear time series analysis

KW - time-series

KW - cygnus X-1

KW - nonlinearity

KW - variability

U2 - 10.1142/S0218127404010527

DO - 10.1142/S0218127404010527

M3 - Article

VL - 14

SP - 2107

EP - 2114

JO - International Journal of Bifurcation and Chaos

JF - International Journal of Bifurcation and Chaos

SN - 0218-1274

IS - 6

ER -