The prediction of financial markets is a challenging yet important task. In modern electronically-driven markets, traditional time-series econometric methods often appear incapable of capturing the true complexity of the multi-level interactions driving the price dynamics. While recent research has established the effectiveness of traditional machine learning (ML) models in financial applications, their intrinsic inability to deal with uncertainties, which is a great concern in econometrics research and real business applications, constitutes a major drawback. Bayesian methods naturally appear as a suitable remedy conveying the predictive ability of ML methods with the probabilistically-oriented practice of econometric research. By adopting a state-of-the-art second-order optimization algorithm, we train a Bayesian bilinear neural network with temporal attention, suitable for the challenging time-series task of predicting mid-price movements in ultra-high-frequency limit-order book markets. We thoroughly compare our Bayesian model with traditional ML alternatives by addressing the use of predictive distributions to analyze errors and uncertainties associated with the estimated parameters and model forecasts. Our results underline the feasibility of the Bayesian deep-learning approach and its predictive and decisional advantages in complex econometric tasks, prompting future research in this direction.

翻译：金融市场预测是一项充满挑战但至关重要的任务。在现代电子化驱动的市场中，传统时间序列计量经济学方法往往难以捕捉驱动价格动态的多层次交互的真正复杂性。尽管近期研究已证实传统机器学习模型在金融应用中的有效性，但其在处理不确定性方面的固有缺陷——这一在计量经济学研究与实际业务中备受关注的问题——构成了重大局限。贝叶斯方法自然成为恰当的解决方案，它将机器学习的预测能力与计量经济学研究以概率为导向的实践相结合。通过采用先进的二阶优化算法，我们训练了一个带有时间注意力机制的贝叶斯双线性神经网络，适用于超高频限价订单簿市场中预测中间价走势这一具有挑战性的时间序列任务。我们通过利用预测分布来分析参数估计与模型预测相关的误差和不确定性，将贝叶斯模型与传统机器学习替代方案进行了全面比较。研究结果凸显了贝叶斯深度学习方法的可行性，及其在复杂计量经济学任务中预测与决策方面的优势，为未来相关研究指明了方向。