We propose a retrodictive forecasting paradigm for time series: instead of predicting the future from the past, we identify the future that best explains the observed present via inverse MAP optimization over a Conditional Variational Autoencoder (CVAE). This conditioning is a statistical modeling choice for Bayesian inversion; it does not assert that future events cause past observations. The approach is theoretically grounded in an information-theoretic arrow-of-time measure: the symmetrized Kullback-Leibler divergence between forward and time-reversed trajectory ensembles provides both the conceptual rationale and an operational GO/NO-GO diagnostic for applicability. We implement the paradigm as MAP inference over an inverse CVAE with a learned RealNVP normalizing-flow prior and evaluate it on six time series cases: four synthetic processes with controlled temporal asymmetry and two ERA5 reanalysis datasets (wind speed and solar irradiance). The work makes four contributions: (i) a formal retrodictive inference formulation; (ii) an inverse CVAE architecture; (iii) a model-free irreversibility diagnostic; and (iv) a falsifiable validation protocol with four pre-specified predictions. All pre-specified predictions are empirically supported: the diagnostic correctly classifies all six cases; the learned flow prior improves over an isotropic Gaussian baseline on GO cases; the inverse MAP yields no spurious advantage on time-reversible dynamics; and on irreversible GO cases, it achieves competitive or superior RMSE relative to forward baselines, with a statistically significant 17.7% reduction over a forward MLP on ERA5 solar irradiance. These results provide a structured proof-of-concept that retrodictive forecasting can constitute a viable alternative to conventional forward prediction when statistical time-irreversibility is present and exploitable.

翻译：我们提出了一种时间序列的回溯性预测范式：不同于从过去预测未来，我们通过条件变分自编码器（CVAE）上的逆最大后验概率优化，识别出最能解释当前观测结果的未来状态。这种条件化是贝叶斯反演的一种统计建模选择，并非断言未来事件导致过去观测。该方法在理论上基于一种信息论的时间箭头度量：正向与时间反转轨迹集合之间的对称化Kullback-Leibler散度既提供了概念依据，也提供了适用性的可操作GO/NO-GO诊断标准。我们将该范式实现为具有学习型RealNVP标准化流先验的逆CVAE上的最大后验概率推断，并在六个时间序列案例上进行了评估：四个具有受控时间不对称性的合成过程，以及两个ERA5再分析数据集（风速和太阳辐照度）。本工作做出了四项贡献：（i）形式化的回溯性推断框架；（ii）逆CVAE架构；（iii）无模型不可逆性诊断方法；（iv）包含四项预先设定预测的可证伪验证方案。所有预先设定的预测均得到实证支持：诊断方法正确分类了全部六个案例；在GO案例中，学习到的流先验优于各向同性高斯基线；在时间可逆动态上，逆最大后验概率推断未产生虚假优势；而在不可逆的GO案例中，相对于前向基线模型，其取得了具有竞争力或更优的均方根误差，其中在ERA5太阳辐照度数据上相比前向多层感知机实现了统计显著的17.7%误差降低。这些结果提供了一个结构化的概念验证，表明当存在统计时间不可逆性且可被利用时，回溯性预测可以构成传统前向预测的可行替代方案。