Time series prediction presents a significant challenge across various domains, such as transportation systems, environmental science, and multiple industrial sectors. Real-world time series data commonly exhibit periodic patterns and irregular sampling rates. Recent advancements in long sequence time series forecasting have made significant progress in adopting deep neural networks, particularly the Transformers, renowned for their robust representational capabilities. However, current Transformer-based models consider time steps as discrete tokens, thereby failing to account for periodicity and temporal intervals when selecting relevant time steps in the past. To address this limitation, we propose an end-to-end framework called Periormer for forecasting irregularly sampled time series. Periormer comprises three key components: (1) a novel input embedding layer that encodes the periodicity and time interval information, analogous to positional encoding in Transformers; (2) a feature-wise periodic attention mechanism that selects essential data points considering the periods and amplitudes of the periodic signals; and (3) a cross-feature periodic attention mechanism that identifies essential features relevant to the prediction. Experiments on four real-world datasets and one synthetic dataset demonstrate that Periormer reduces the mean squared error by 14.9% compared to state-of-the-art models.

Missing data imputation for location-based sensor data has attracted much attention in recent years. The state-of-the-art imputation methods based on graph neural networks have a priori assumption that the spatial correlations between sensor locations are static. However, real-world data sets often exhibit dynamic spatial correlations. This paper proposes a novel approach to capturing the dynamics of spatial correlations between geographical locations as a composition of the constant, long-term trends and periodic patterns. To this end, we design a new method called Dynamic Adjacency Matrix Representation (DAMR) that extracts various dynamic patterns of spatial correlations and represents them as adjacency matrices. The adjacency matrices are then aggregated and fed into a well-designed graph representation learning layer for predicting the missing values. Through extensive experiments on six real-world data sets, we demonstrate that DAMR reduces the MAE by up to 19.4% compared with the state-of-the-art methods for the missing value imputation task