Forecasting bubbles with mixed causal-noncausal autoregressive models

This paper investigates one-step ahead density forecasts of mixed causal-noncausal models. We compare the sample-based and the simulations-based approaches respectively developed by Gouriéroux and Jasiak (2016) and Lanne, Luoto, and Saikkonen (2012). We focus on explosive episodes and therefore on predicting turning points of bubbles bursts. We suggest the use of both methods to construct investment strategies based on how much probabilities are induced by the assumed model and by past behaviours. We illustrate our analysis on Nickel prices series.