The identification of nonlinear biological systems: Wiener and Hammerstein cascade models
Biological Cybernetics
Testing for nonlinearity in time series: the method of surrogate data
Conference proceedings on Interpretation of time series from nonlinear mechanical systems
Physica D
Nonlinear system identification using autoregressive quadratic models
Signal Processing
Neural Computation
Improved bispectrum based tests for Gaussianity and linearity
Signal Processing
Nonlinear system identification: an effective framework based on the Karhunen-Loève transform
IEEE Transactions on Signal Processing
A stability condition for certain bilinear systems
IEEE Transactions on Signal Processing
The quality of models for ARMA processes
IEEE Transactions on Signal Processing
Asymptotic MAP criteria for model selection
IEEE Transactions on Signal Processing
Linear multichannel blind equalizers of nonlinear FIR Volterrachannels
IEEE Transactions on Signal Processing
Polyspectrum modeling using linear or quadratic filters
IEEE Transactions on Signal Processing
Hypothesis Testing for Nonlinearity Detection Based on an MA Model
IEEE Transactions on Signal Processing
A blind approach to the Hammerstein-Wiener model identification
Automatica (Journal of IFAC)
Identification of linear systems with nonlinear distortions
Automatica (Journal of IFAC)
| Hi-index | 0.08 |
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.