Discrimination power of measures for nonlinearity in a time series

The performance of a number of different measures of nonlinearity in a time series is compared numerically. Their power to distinguish noisy chaotic data from linear stochastic surrogates is determined by Monte Carlo simulation for a number of typical data problems. The main result is that the ratings of the different measures vary from example to example. It therefore seems preferable to use an algorithm with good overall performance, that is, higher order autocorrelations or nonlinear prediction errors.