Tail-Aware Density Forecasting of Locally Explosive Time Series: A Neural Network Approach

Elena Dumitrescu; Julien Peignon; Arthur Thomas

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arXiv · 2601.14049

Tail-Aware Density Forecasting of Locally Explosive Time Series: A Neural Network Approach

Elena Dumitrescu·Julien Peignon·Arthur Thomas

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Abstract

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 non-causal forecasts while remaining computationally tractable. Monte Carlo experiments and a real-time natural-gas application show substantial improvements over existing density-forecasting methods.

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BibTeX RIS

Elena Dumitrescu, Julien Peignon, Arthur Thomas. 2026-01-20. Tail-Aware Density Forecasting of Locally Explosive Time Series: A Neural Network Approach. https://arxiv.org/abs/2601.14049

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