It may be late. But researchers and students can found some useful literature and MATLAB functions for nonlinearity test for time series datasets. For details, one can refer to:
Harvey, D. I. and S. J. Leybourne (2007). "Testing for time series linearity." The Econometrics Journal 10(1): 149-165.
Berg, A., et al. (2010). "A bootstrap test for time series linearity." Journal of Statistical Planning and Inference 140(12): 3841-3857.
Furthermore, some free MATLAB functions are available:
https://www.mathworks.com/matlabcentral/fileexchange/16062-test-of-non-linearity based the following article (Barnett, A. G. and R. C. Wolff (2005). "A time-domain test for some types of nonlinearity." IEEE Transactions on Signal Processing 53(1): 26-33.)
https://www.mathworks.com/matlabcentral/fileexchange/27561-measures-of-analysis-of-time-series-toolkit--mats- based on the following article (Kugiumtzis, D. and A. Tsimpiris (2010). "Measures of analysis of time series (MATS): A MATLAB toolkit for computation of multiple measures on time series data bases." Journal of Statistical Software 33(5).)
