  Measuring the predictability and complexity of time series using entropy is
essential tool de-signing and controlling a nonlinear system. However, the
existing methods have some drawbacks related to the strong dependence of
entropy on the parameters of the methods. To overcome these difficulties, this
study proposes a new method for estimating the entropy of a time series using
the LogNNet neural network model. The LogNNet reservoir matrix is filled with
time series elements according to our algorithm. The accuracy of the
classification of images from the MNIST-10 database is considered as the
entropy measure and denoted by NNetEn. The novelty of entropy calculation is
that the time series is involved in mixing the input information in the
res-ervoir. Greater complexity in the time series leads to a higher
classification accuracy and higher NNetEn values. We introduce a new time
series characteristic called time series learning inertia that determines the
learning rate of the neural network. The robustness and efficiency of the
method is verified on chaotic, periodic, random, binary, and constant time
series. The comparison of NNetEn with other methods of entropy estimation
demonstrates that our method is more robust and accurate and can be widely used
in practice.
