The probability prediction of multivariate time series is a notoriously challenging but practical task. On the one hand, the challenge is how to effectively capture the cross-series correlations between interacting time series, to achieve accurate distribution modeling. On the other hand, we should consider how to capture the contextual information within time series more accurately to model multivariate temporal dynamics of time series. In this work, we proposed a novel non-autoregressive deep learning model, called Multi-scale Attention Normalizing Flow(MANF), where we integrate multi-scale attention and relative position information and the multivariate data distribution is represented by the conditioned normalizing flow. Additionally, compared with autoregressive modeling methods, our model avoids the influence of cumulative error and does not increase the time complexity. Extensive experiments demonstrate that our model achieves state-of-the-art performance on many popular multivariate datasets.

翻译：多元时间序列的概率预测是一项极具挑战性但具有实用价值的任务。一方面，挑战在于如何有效捕捉交互时间序列间的跨序列相关性，以实现精确的分布建模。另一方面，需要考虑如何更准确地捕捉时间序列内部的上下文信息，以建模多元时间序列的时域动态特性。本研究提出了一种新颖的非自回归深度学习模型——多尺度注意力归一化流（Multi-scale Attention Normalizing Flow，MANF），该模型整合了多尺度注意力与相对位置信息，并通过条件归一化流来表示多元数据分布。此外，与自回归建模方法相比，我们的模型避免了累积误差的影响，且未增加时间复杂度。大量实验表明，我们的模型在多个主流多元数据集上达到了最先进的性能。