Abstract
The analytical properties of the solution of a system of ODEs in the complex time plane influence its dynamical behavior on the real time axis. In particular, the extrema of the real time solution can be associated to the singularities of the complex solution falling close to the real time axis. Moreover for a twice differentiable stochastic process, the expected value of the number of extrema for unit time can be determined. These two results are used here as the starting point to introduce two new algorithms to test for time series nonlinearity. They do not require the phase space reconstruction protocol and seem to work well also for short data sets.
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