论文标题
使用神经网络体系结构进行时间序列建模支持最佳相位空间重建
Supporting Optimal Phase Space Reconstructions Using Neural Network Architecture for Time Series Modeling
论文作者
论文摘要
相位空间的重建是根据动态系统概念分析时间序列的重要步骤。在此类空间上执行的回归揭示了系统状态之间的关系，我们可以从中得出它们的生成规则，即最可能沿时间生成观察值的最可能的功能集。从这个意义上讲，大多数方法都依赖于Takens的嵌入定理来展开相位空间，这需要嵌入维度和时间延迟。此外，尽管已经提出了几种方法来从经验上估算这些参数，但由于缺乏一致性和鲁棒性，它们仍然面临局限性，这激发了本文。作为替代方案，我们在这里提出一个具有遗忘机制的人工神经网络，以隐式地学习相位空间的属性。此类网络训练预测错误，并在收敛之后，将其架构用于估计嵌入参数。实验结果证实，我们的方法要么比大多数最先进的策略具有竞争力或更好的竞争力，同时揭示了时间序列观察之间的时间关系。
The reconstruction of phase spaces is an essential step to analyze time series according to Dynamical System concepts. A regression performed on such spaces unveils the relationships among system states from which we can derive their generating rules, that is, the most probable set of functions responsible for generating observations along time. In this sense, most approaches rely on Takens' embedding theorem to unfold the phase space, which requires the embedding dimension and the time delay. Moreover, although several methods have been proposed to empirically estimate those parameters, they still face limitations due to their lack of consistency and robustness, which has motivated this paper. As an alternative, we here propose an artificial neural network with a forgetting mechanism to implicitly learn the phase spaces properties, whatever they are. Such network trains on forecasting errors and, after converging, its architecture is used to estimate the embedding parameters. Experimental results confirm that our approach is either as competitive as or better than most state-of-the-art strategies while revealing the temporal relationship among time-series observations.
