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# Testing for nonlinearity

Most of the methods and quantities discussed so far are most appropriate in cases where the data show strong and consistent nonlinear deterministic signatures. As soon as more than a small or at most moderate amount of additive noise is present, scaling behavior will be broken and predictability will be limited. Thus we have explored the opposite extreme, nonlinear and fully deterministic, rather than the classical linear stochastic processes. The bulk of real world time series falls in neither of these limiting categories because they reflect nonlinear responses and effectively stochastic components at the same time. Little can be done for many of these cases with current methods. Often it will be advisable to take advantage of the well founded machinery of spectral methods and venture into nonlinear territory only if encouraged by positive evidence. This section is about methods to establish statistical evidence for nonlinearity beyond a simple rescaling in a time series.

- The concept of surrogate data
- Iterative Fourier transform method
- General constrained randomization
- Measuring weak nonlinearity

Next: The concept of surrogate Up: Practical implementation of nonlinear Previous: Entropy estimates