Tail-Aware Density Forecasting of Locally Explosive Time Series: A Neural Network Approach
Elena Dumitrescu, Julien Peignon, Arthur Thomas
TL;DR
This paper tackles density forecasting for time series with locally explosive dynamics, where noncausal MARMA models are theoretically appealing but challenging to forecast. It introduces a Mixture Density Network with skewed-t components, an adaptive tail-weighting scheme, and post-hoc local PIT calibration to produce accurate, near-instantaneous conditional densities $p(X_{t+h}|oldsymbol{X}_t)$ across horizons. The method demonstrates superior performance relative to kernel density, simulation-based, and other learning-based approaches in extensive Monte Carlo simulations and in real-time natural gas price forecasting, especially in the tails and for multimodal densities. The framework offers substantial practical value for risk assessment and decision-making in finance by delivering fast, calibrated density forecasts that adapt to extreme events and bubble-like behavior in asset prices.
Abstract
This paper proposes a Mixture Density Network for forecasting time series that exhibit locally explosive behavior. By incorporating skewed t-distributions as mixture components, our approach offers enhanced flexibility in capturing the skewed, heavy-tailed, and potentially multimodal nature of predictive densities associated with bubble dynamics modeled by mixed causal-noncausal ARMA processes. In addition, we implement an adaptive weighting scheme that emphasizes tail observations during training and hence leads to accurate density estimation in the extreme regions most relevant for financial applications. Equally important, once trained, the MDN produces near-instantaneous density forecasts. Through extensive Monte Carlo simulations and an empirical application on the natural gas price, we show that the proposed MDN-based framework delivers superior forecasting performance relative to existing approaches.