Abstract
The surrogates approach was suggested as a means to distinguish linear from nonlinear stochastic or deterministic processes. The numerical implementation is straightforward, but the statistical interpretation depends strongly on the stochastic process under consideration and the used test statistic. In the first part, we present quantitative investigations of level accuracy under the null hypothesis, power analysis for several violations, properties of phase randomization, and examine the assumption of uniformly distributed phases. In the second part we focus on level accuracy and power characteristics of Amplitude Adjusted Fourier-Transformed (AAFT) and improved AAFT (IAAFT) algorithms. In our study AAFT outperforms IAAFT. The latter method has a similar performance in many setups but it is not stable in general. We will see some examples where it breaks down.
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Maiwald, T., Mammen, E., Nandi, S., Timmer, J. (2008). Surrogate Data — A Qualitative and Quantitative Analysis. In: Dahlhaus, R., Kurths, J., Maass, P., Timmer, J. (eds) Mathematical Methods in Signal Processing and Digital Image Analysis. Understanding Complex Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75632-3_2
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DOI: https://doi.org/10.1007/978-3-540-75632-3_2
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