Effective and Efficient Incomplete Multivariate Time Series Forecasting

The missing values widely existing in multivariate time series significantly hinder accurate forecasting efforts. Existing multivariate time series forecasting methods predominantly learn the interrelations between complete historical and future time series data, thus failing to accommodate the prevalent instances of missing values within these time series data. In this paper, we propose a novel forecasting model, named Enter, which integrates two key modules, i.e., missing-aware pre-training (MAP) and incomplete time series forecasting (ITF), to forecast incomplete multivariate time series effectively and efficiently in an end-to-end manner. Specifically, MAP introduces a missing-aware Transformer to pre-train the forecasting model by learning the underlying data distribution from incomplete historical multivariate time series. ITF fine-tunes this pre-trained model with a cross attention mechanism to robustly forecast future time series without error accumulation by leveraging all observed elements within the historical multivariate time series. Extensive experiments on four real-world multivariate time series datasets and a publicly available incomplete meteorological dataset demonstrate that, compared with the state-of-the-art methods, Enter yields over a more than 21% accuracy gain. It accelerates the training process up to two orders of magnitude faster.