Using surrogate data to test for nonlinearity in experimental

| The technique of surrogate data provides has been used to test for membership of particular classes of linear systems. Existing algorithms provide non-parametric methods to generate surrogates similar to the data and consistent with a given hypothesis. These non-parametric methods allow a wide range of test statistics to be utilized. We suggest an obvious extension of this to classes of nonlinear para-metric models. To do so it is necessary to restrict the statistics employed to a relatively broad class. We demonstrate that correlation dimension provides a suitable statistic and apply these methods, together with existing surrogate tests to respiratory data from sleeping infants. Although our data are clearly distinct from the diierent classes of linear systems we are unable to distinguish between our data and surrogates generated by nonlinear models. Hence we conclude that our data cannot be explained by linearly ltered noise but is consistent with the noisy periodic orbit of a nonlinear system.