Measuring the predictability and complexity of time series is an essential tool in designing and controlling the nonlinear system. There exist different entropy measures in the literature to analyze the predictability and complexity of time series. However, these measures have some drawbacks especially in short time series. To overcome the difficulties, this paper proposes a new method for estimating the entropy of a time series using the LogNNet 784:25:10 neural network model. The LogNNet reservoir matrix consists of 19625 elements which is filled with the time series elements. After that, 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. A more complex transformation of the input information by the time series in the reservoir leads to higher NNetEn values. Many practical time series data have less than 19625 elements. Some duplicating or stretching methods are investigated to overcome this difficulty and the most successful method is identified for practical applications. The epochs number in the training process of LogNNet is considered as the input parameter. A new time series characteristic called time series learning inertia is introduced to investigate the effect of epochs number in the efficiency of neural network. To show the robustness and efficiency of the proposed method, it is applied on some chaotic, periodic, random, binary and constant time series. The NNetEn is compared with some existing entropy measures. The results show that the proposed method is more robust and accurate than existing methods.

中文翻译：

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一种利用人工神经网络估计时间序列熵的方法

测量时间序列的可预测性和复杂性是设计和控制非线性系统的重要工具。文献中存在不同的熵度量来分析时间序列的可预测性和复杂性。然而，这些措施有一些缺点，特别是在短时间序列中。为了克服这些困难，本文提出了一种使用 LogNNet 784:25:10 神经网络模型估计时间序列熵的新方法。LogNNet 储层矩阵由 19625 个元素组成，其中填充了时间序列元素。之后，在 MNIST-10 数据集上训练网络并计算分类精度。准确度被认为是熵度量，用 NNetEn 表示。通过储层中的时间序列对输入信息进行更复杂的转换会导致更高的 NNetEn 值。许多实用的时间序列数据少于 19625 个元素。研究了一些复制或拉伸方法来克服这个困难，并确定了实际应用中最成功的方法。LogNNet 训练过程中的 epochs 数被视为输入参数。引入了一种称为时间序列学习惯性的新时间序列特征来研究纪元数对神经网络效率的影响。为了显示所提出方法的鲁棒性和效率，将其应用于一些混沌、周期性、随机、二进制和常数时间序列。NNetEn 与一些现有的熵度量进行了比较。