Estimating Lyapunov exponents on a noisy environment by global and local Jacobian indirect algorithms

Highlights：

• Two new computational algorithms are proposed for estimating the Lyapunov exponents from time series data in order to test the null hypothesis of a chaotic behavior.

• The results obtained provide robust evidence that the Jacobian indirect methods provide better estimates than traditional direct methods in all the experiments we have conducted.

• We have shown empirically that the algorithms proposed are robust to the presence of (small) measurement errors because the results obtained are comparable to those which are noise free.

• The empirical size of the algorithms proposed decreased and the empirical power increased as the sample size increased which means that our hypothesis tests are consistent and reliable.

• This paper opens a new research line where new contributions may appear considering new machine learning methods and deep learning algorithms for estimating the Lyapunov exponents from time series data.