MSDIPN: Multi-scale Deep Interval Prediction Network for Multivariate Time Series

Interval prediction is crucial in decision-making processes across many domains. Although significant progress has been made in existing interval prediction methods, they still face several challenges, such as assumptions about data distribution, fixed interval widths, limitations of gradient-based optimization algorithm, crossing of upper and lower bounds, and insufficient consideration of multi-scale spatial-temporal patterns. To address these issues, we propose a Multi-Scale Deep Interval Prediction Network (MSDIPN). Specifically, a Multi-Scale Spatio-Temporal Self-Attention Mechanism is introduced to capture spatio-temporal dependencies across different spatial scales. Additionally, a Temporal Self-Attention Mechanism module is constructed to extract temporal dependencies of historical variables across varying lag phases. Then a Global Self-Attention Mechanism module is designed to address representation degradation using residual connections and self-attention mechanisms. To overcome limitations related to distributional assumptions, fixed interval widths, and crossing problems, an Improved LUBE module is developed as the output module for generating prediction intervals (PIs) of time series data. Furthermore, a gradient-based PIs loss function is designed to address the optimization issue of MSDIPN by integrating a smooth approximation function with a pinball loss function.