Fusion of hypothesis testing for nonlinearity detection in small time series

The performances of parametric or non-parametric Hypothesis Testing (HT) for nonlinearity detection are fairly weak for small time series (typically between 128 and 512 samples). A natural idea to improve the results is to merge several HT to make a more robust decision. In this paper, we inspect the topology to perform this fusion. However three steps are needed before optimizing this fusion process. The first one is a rigorous estimate of the robustness of the 12 selected HT in order to only keep the more robust ones. The second one is the validation of the surrogate data method to estimate the index pdf under H-0 (i.e. the observed time series is "linear"). In fact, this pdf is necessary to define the threshold to accept/reject the null hypothesis of linearity. The last step is also an estimate of the mutual information between the indices involved in the fusion process, since the fusion of close indices cannot improve the decision. Numerical results show that the method of fusion changes when the time series length increases. (C) 2012 Elsevier B.V. All rights reserved.