Interval wavelets based multiscale normalizing flow for forecasting irregularly sampled time series (IWMNF)

Abstract This work addresses the problem of probabilistic forecasting of irregular multivariate time series (IMTS), a common scenario in domains such as healthcare, climate, and economics, characterized by heterogeneous sampling and missing values. Traditional statistical methods and deep learning techniques, although effective in certain contexts, face limitations when dealing with nonlinearities and dynamic dependencies among variables. Recent studies indicate that graph-based architectures, normalizing flows, and wavelet transforms can help overcome these limitations, however they have not been unified into a single model. To fill this gap, we propose a probabilistic framework that combines graph-based representations, invertible normalizing flows, and multiresolution decompositions via wavelets, aiming to estimate the joint distribution of IMTS. The method is evaluated on three real-world datasets from the medical and climate domains and compared against benchmark models from the literature. The results demonstrate improvements in predictive accuracy. To the best of our knowledge, this is the first work to integrate graph structures and wavelets within a unified normalizing flow, opening new perspectives for future applications such as imputation and anomaly detection.