An elementary Recurrent Neural Network that operates on p time lags, called an RNN(p), is the natural generalisation of a linear autoregressive model ARX(p). It is a powerful forecasting tool for variables displaying inherent seasonal patterns across multiple time scales, as is often observed in energy, economic, and financial time series. The architecture of RNN(p) models, characterised by structured feedbacks across time lags, enables the design of efficient training strategies. We conduct a comparative study of learning algorithms for these models, providing a rigorous analysis of their computational complexity and training performance. We present two applications of RNN(p) models in power consumption forecasting, a key domain within the energy sector where accurate forecasts inform both operational and financial decisions. Experimental results show that RNN(p) models achieve excellent forecasting accuracy while maintaining a high degree of interpretability. These features make them well-suited for decision-making in energy markets and other fintech applications where reliable predictions play a significant economic role.

翻译：一种基于p个时间滞后的基本循环神经网络，称为RNN(p)，是线性自回归模型ARX(p)的自然推广。对于在多个时间尺度上表现出固有季节性模式的变量（常见于能源、经济和金融时间序列），RNN(p)是一种强大的预测工具。该模型架构具有跨时间滞后的结构化反馈特性，使得设计高效训练策略成为可能。我们对这些模型的学习算法进行了比较研究，对其计算复杂度和训练性能进行了严格分析。我们展示了RNN(p)模型在电力消费预测中的两个应用案例——这是能源领域的关键方向，精准预测直接影响运营与金融决策。实验结果表明，RNN(p)模型在保持高度可解释性的同时实现了优异的预测精度。这些特性使其特别适用于能源市场决策及其他金融科技应用场景，在这些领域中可靠的预测具有显著的经济价值。