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Title: Forecasting heavy-tailed noncausal processes and bubble crash odds Authors:  Sebastien Fries - Vrije Universiteit Amsterdam (Netherlands) [presenting]
Abstract: Noncausal or anticipative, heavy-tailed processes generate trajectories featuring locally explosive episodes akin to speculative bubbles in financial time series data. For $X_t$, a two-sided infinite alpha-stable moving average, conditional moments up to integer-order four are shown to exist provided $X_t$ is anticipative enough, despite the process featuring infinite marginal variance. Formulae of these moments at any forecast horizon under any admissible parameterisation are provided. Under the assumption of errors with regularly varying tails, closed-form formulae of the predictive distribution during explosive bubble episodes are obtained, and expressions of the ex-ante crash odds at any horizon are available. It is found that the noncausal autoregression of order 1 (AR(1)) with AR coefficient $\rho$ and tail exponent $\alpha$ generates bubbles whose survival distributions are geometric with parameter $\rho^{\alpha}$. This property extends to bubbles with arbitrarily-shaped collapse after the peak, provided the inflation phase is noncausal AR(1)-like. It appears that mixed causal-noncausal processes generate explosive episodes with certain dynamics which could reconcile rational bubbles with tail exponents greater than 1. The use of the conditional moments is illustrated in a bubble-timing portfolio allocation framework, and an application of the closed-form predictive crash odds to the Nasdaq and S\&P500 series is provided.