A method for estimating the entropy of time series using artificial neural network

Measuring the predictability and complexity of time series is an essential tool in designing and controlling the nonlinear system. Different entropy measures exist in the literature to analyze the predictability and complexity of time series. However, the existed methods have some drawbacks related to a strong dependence of entropy on the parameters of the methods, as well as on the length and amplitude of the time series. 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 the time series elements according to our algorithm. The network is trained on MNIST-10 dataset and the classification accuracy is calculated. The accuracy 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 reservoir. The greater complexity of the time series leads to the better ability of the neural network to learn, and to the higher classification accuracy and NNetEn values. The epochs number in the training process of LogNNet is considered as the control parameter. 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.