Retrodictive Forecasting: A Proof-of-Concept for Exploiting Temporal Asymmetry in Time Series Prediction

TL;DR

The 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.

Abstract

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.

Figures (13)

• Figure 1: Training curves (ELBO loss) for all six cases. Solid: training loss; dashed: validation loss. Stable convergence without overfitting across all cases confirms correct CVAE training.
• Figure 2: Cross-case RMSE comparison (all six cases, five methods). The inverse MAP (flow, green) is competitive or best on all GO cases, while the forward MLP (orange) clearly dominates on Case B (NO-GO). Case D shows near-perfect equivalence across methods.
• Figure 3: RMSE per forecast horizon $h \in \{1, \ldots, 16\}$ for all six cases and five methods. GO cases (A, C, ERA5, ERA_ssrd): the inverse MAP with flow prior (dark green) is competitive with or below the forward MLP (orange) across most horizons, with the advantage widening at longer horizons on ERA_ssrd. NO-GO cases (B, D): the forward MLP dominates on Case B; Case D shows near-equivalence consistent with time-reversibility. The N(0,I) prior (pink) uniformly underperforms the flow prior on GO cases. Compare with Fig. \ref{['fig:10']} (GO cases only, overlay).
• Figure 4: Falsifiable predictions scorecard. All 4/4 predictions PASS. Summary panel produced by the automated verification module.
• Figure 5: Arrow-of-time diagnostic (block permutation test) for all six cases. Top panels: $J_{\mathrm{obs}}(w)$ at $w = 2, 4, 8$ for LEVEL (left) and DIFF (right) representations. Bottom panels: $-\log_{10}(p)$ with the $\alpha = 0.05$ threshold (red dashed). GO cases (A, C, ERA5, ERA_ssrd) exceed the threshold; NO-GO cases (B, D) remain below. Case C dominates with $J_{\mathrm{obs}}$ up to 22.9 in LEVEL; ERA_ssrd leads in DIFF with $J_{\mathrm{obs}} = 5.3$.