Explosive Bubble Modelling by Noncausal Process

The linear mixed causal and noncausal autoregressive processes provide often a better fit to economic and financial time series than the standard causal linear autoregressive processes. By considering the example of the noncausal Cauchy autoregressive process, we show that it might be explained by the special associated nonlinear causal dynamics. Indeed, this causal dynamics can include unit root, bubble phenomena, or asymmetric cycles often observed on financial markets. The noncausal Cauchy autoregressive process provides a new modelling for explosive multiple bubbles and their transmission in a multivariate dynamic framework. We also explain why standard unit root tests will fail in detecting such explosive bubbles