LAUSR

This paper introduces VAEneu, a novel autoregressive method for multistep ahead univariate probabilistic time series forecasting, designed to address the challenges of generating sharp and well-calibrated probabilistic forecasts without assuming a specific parametric form for the predictive distribution. VAEneu leverages the Conditional VAE framework and optimizes the likelihood of the predictive distribution using the Continuous Ranked Probability Score (CRPS), a strictly proper scoring rule, as the loss function. This approach enables the model to learn flexible, sharp, and well-calibrated predictive distributions without the need for a tractable likelihood function. In a comprehensive empirical study, VAEneu is rigorously benchmarked against 12 baseline models across 12 datasets, demonstrating superior performance in both forecasting accuracy and uncertainty quantification. VAEneu provides a valuable tool for quantifying future uncertainties, and our extensive empirical study lays the foundation for future comparative studies for univariate multistep ahead probabilistic forecasting.