Testing for nonlinearity in time series: the method of surrogate data
Conference proceedings on Interpretation of time series from nonlinear mechanical systems
Numerical recipes in C (2nd ed.): the art of scientific computing
Numerical recipes in C (2nd ed.): the art of scientific computing
Nonlinear time series analysis
Nonlinear time series analysis
Physica D
The Kernel-Adatron Algorithm: A Fast and Simple Learning Procedure for Support Vector Machines
ICML '98 Proceedings of the Fifteenth International Conference on Machine Learning
Kernel independent component analysis
The Journal of Machine Learning Research
Generalized correlation function: definition, properties, and application to blind equalization
IEEE Transactions on Signal Processing - Part I
A test of independence based on a generalized correlation function
Signal Processing
Neural data analysis and reduction using improved framework of information-preserving EMD
IDEAL'10 Proceedings of the 11th international conference on Intelligent data engineering and automated learning
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Nonlinearity tests have become an essential step in system analysis and modeling due to the computational demands and complexity of analysis involved in nonlinear modeling. Standard nonlinear measures are either too complicated to estimate accurately (such as Lyapunov exponents and correlation dimension), or not able to capture sufficient but not necessary conditions of nonlinearity (such as time asymmetry). Correntropy is a kernel-based similarity measure which contains the information of both statistical and temporal structure of the underlying dataset. The capability of preserving nonlinear characteristics makes correntropy a suitable candidate as a measure for determining nonlinear dynamics. Moreover, since correntropy makes use of kernel methods, its estimation is computationally efficient. Using correntropy as the test statistic, nonlinearity tests based on the null hypothesis that signals of interest are realizations of linear Gaussian stochastic processes are carried out via surrogate data methods. Experiments performed on linear Gaussian, linear non-Gaussian, and nonlinear systems with varying in-band noise levels, data lengths, and kernel sizes confirm that correntropy can be employed as a discriminative measure for detecting nonlinear characteristics in time series. Results of tests performed on data collected from natural systems are in agreement with findings in time series analysis literature.