A0403
Title: Prediction of bubbles in presence of alpha-stable aggregates moving averages
Authors: Arthur Thomas - Paris Dauphine University - PSL (France) [presenting]
Gilles De Truchis - University of Orleans (France)
Sebastien Fries - Vrije Universiteit Amsterdam (Netherlands)
Abstract: Financial markets frequently exhibit boom-and-bust cycles that are incompatible with standard linear time series models. While anticipative heavy-tailed linear processes offer a promising alternative for modeling such phenomena, they impose uniform bubble patterns across different episodes, contradicting empirical evidence. A new model is introduced based on alpha-stable moving average aggregates that accommodates heterogeneous bubble dynamics. The theoretical properties of this model are established, demonstrating that it admits a semi-norm representation on a unit cylinder, thereby enabling the prediction of extreme trajectories with varying growth dynamics. A minimum distance estimation procedure is developed based on the joint characteristic function, and its asymptotic properties are established. Monte Carlo simulations confirm the estimator's good finite-sample performance across various specifications. The empirical application to the CBOE Crude Oil ETF Volatility Index successfully decomposes observed volatility dynamics into distinct components with different persistence properties, revealing that what appears as a single bubble episode actually consists of multiple superimposed processes with heterogeneous growth rates and crash probabilities.
