This paper proposes a Mixture Density Network specifically designed 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 two empirical applications, on the natural gas price and inflation, we show that the proposed MDN-based framework delivers superior forecasting performance relative to existing approaches.

翻译：本文提出一种专门为预测呈现局部爆炸性行为的时间序列而设计的混合密度网络。通过引入偏斜t分布作为混合分量，我们的方法在捕捉由混合因果-非因果ARMA过程建模的泡沫动态所关联的预测密度之偏斜、厚尾及潜在多模态特性方面，提供了更强的灵活性。此外，我们实现了一种自适应加权方案，该方案在训练过程中强调尾部观测值，从而在最相关于金融应用的极端区域实现精确的密度估计。同样重要的是，一旦训练完成，该混合密度网络可产生近乎瞬时的密度预测。通过大量的蒙特卡洛模拟以及在天然气价格和通货膨胀率上的两项实证应用，我们表明，所提出的基于混合密度网络的框架相较于现有方法，能提供更优的预测性能。