Forecasting bubbles with mixed causal-noncausal autoregressive models

Density forecasts of locally explosive processes are investigated using mixed causal-noncausal models, namely time series models with both lag and lead components. In the absence theoretical expressions for predictive density a large range potential error distributions, two approximation methods analysed compared Monte Carlo simulations. The focus is on prediction one-step ahead probabilities turning points during bubble episodes. A thorough analysis provides some guidance in these extreme events, suggestion to consider approaches together as they jointly carry more information. illustrated an application Nickel prices, focusing financial crisis bubble.