  The performance of recurrence networks and symbolic networks to detect weak
nonlinearities in time series is compared to the nonlinear prediction error.
For the synthetic data of the Lorenz system, the network measures show a
comparable performance. In the case of relatively short and noisy real-world
data from active galactic nuclei, the nonlinear prediction error yields more
robust results than the network measures. The tests are based on surrogate data
sets. The correlations in the Fourier phases of data sets from some surrogate
generating algorithms are also examined. The phase correlations are shown to
have an impact on the performance of the tests for nonlinearity.
