This paper presents VAEneu, an innovative autoregressive method for multistep ahead univariate probabilistic time series forecasting. We employ the conditional VAE framework and optimize the lower bound of the predictive distribution likelihood function by adopting the Continuous Ranked Probability Score (CRPS), a strictly proper scoring rule, as the loss function. This novel pipeline results in forecasting sharp and well-calibrated predictive distribution. Through a comprehensive empirical study, VAEneu is rigorously benchmarked against 12 baseline models across 12 datasets. The results unequivocally demonstrate VAEneu's remarkable forecasting performance. 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.

翻译：本文提出VAEneu，一种用于单变量多步向前概率时间序列预测的创新性自回归方法。我们采用条件变分自编码器框架，并以严格恰当评分准则——连续排序概率得分（CRPS）作为损失函数，优化预测分布似然函数的下界。这一新颖的流水线能够生成陡峭且校准良好的预测分布。通过全面的实证研究，我们在12个数据集上对VAEneu与12个基线模型进行了严格基准测试。结果明确证明了VAEneu卓越的预测性能。VAEneu为量化未来不确定性提供了宝贵工具，而本研究的广泛实证分析也为未来单变量多步向前概率预测的比较研究奠定了基础。