Calibrated Probabilistic Forecasting of Heavy-Tailed Financial Returns via Spiking Neural Networks with Dynamic Adaptive Computation

Abstract

Probabilistic forecasting of financial time series demands models that simultaneously capture heavy-tailed return distributions, time-varying volatility, and structural regime changes. Classical econometric models provide interpretable but rigid parametric specifications, while modern deep forecasting architectures achieve flexibility at the cost of substantial computational overhead. This paper introduces a novel spiking neural network augmented with dynamic adaptive computation for energy-efficient probabilistic sequence modeling. The proposed architecture processes sequential inputs through a leaky integrate-and-fire backbone with learnable, activity-dependent firing thresholds inspired by biological synaptic scaling, outputting the parameters of a Student-t distribution with input-dependent degrees of freedom. The experimental protocol employs a strict chronological train-test split to prevent data leakage. Evaluated across seven synthetic and empirical financial datasets, achieves aggregate calibration comparable to the best-performing fixed-threshold spiking baseline while substantially improving upon the classical and dense neural baselines. Specifically, it shares the lowest Mean Absolute Coverage Error of one point two zero percentage points, with statistical tests confirming significant improvements in coverage and continuous ranked probability score on heavy-tailed assets like Bitcoin. While dense baselines achieve competitive point accuracy, they exhibit severe under-coverage on these assets. In contrast, the proposed approach maintains robust calibration during extreme market regimes, as validated by formal Value-at-Risk backtests supplemented by Expected Shortfall diagnostics. Regime-stratified evaluation demonstrates that the adaptive threshold mechanism prevents the catastrophic over-coverage of classical models during high-volatility crises. Computational analysis indicates that the event-driven architecture maintains sparse spike activity, translating into an estimated ninety-eight point three percent reduction in the analytical software-level energy proxy compared to dense inference baselines. Downstream applications to volatility tracking and unsupervised anomaly detection validate the practical utility of these predictive distributions for real-time risk management, paving the way for resource-efficient models on future neuromorphic hardware.