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