You can build prediction sets for time series that adapt to learned dependencies between variables while guaranteeing coverage, by combining neural filters with conformal calibration—no need to assume Gaussian tails.
This paper develops a method for creating prediction sets (confidence regions) for multivariate time series that properly account for dependencies between variables. It combines a learned state-space filter that predicts future values and their uncertainty with conformal calibration—a distribution-free technique that guarantees coverage.