Working papers

Tail-aware density forecasting of locally explosive time series: a neural network approach. Dumitrescu, E., Peignon, J., Thomas, A. (2026) [working paper] [online appendix] [replication code] Submitted

Mixed causal–noncausal (anticipative) models capture locally explosive dynamics and provide economically meaningful probabilities of continuation and collapse, but forecasting with them remains computationally difficult. We develop a two-stage framework that estimates such an ARMA model and then learns its predictive density using a Mixture Density Network with skewed-t components, tail-aware training weights, and post-hoc calibration. The approach accommodates the heavy tails, asymmetry, and multimodality characteristic of noncausal forecasts while remaining computationally tractable. Monte Carlo experiments and a real-time natural-gas application show substantial improvements over existing density-forecasting methods.