TDT Loss Takes It All: Integrating Temporal Dependencies among Targets into Non-Autoregressive Time Series Forecasting

Learning temporal dependencies among targets (TDT) benefits better time series forecasting, where targets refer to the predicted sequence. Although autoregressive methods model TDT recursively, they suffer from inefficient inference and error accumulation. We argue that integrating TDT learning into non-autoregressive methods is essential for pursuing effective and efficient time series forecasting. In this study, we introduce the differencing approach to represent TDT and propose a parameter-free and plug-and-play solution through an optimization objective, namely TDT Loss. It leverages the proportion of inconsistent signs between predicted and ground truth TDT as an adaptive weight, dynamically balancing target prediction and fine-grained TDT fitting. Importantly, TDT Loss incurs negligible additional cost, with only $\mathcal{O}(n)$ increased computation and $\mathcal{O}(1)$ memory requirements, while significantly enhancing the predictive performance of non-autoregressive models. To assess the effectiveness of TDT loss, we conduct extensive experiments on 7 widely used datasets. The experimental results of plugging TDT loss into 6 state-of-the-art methods show that out of the 168 experiments, 75.00\% and 94.05\% exhibit improvements in terms of MSE and MAE with the maximum 24.56\% and 16.31\%, respectively.