Modeling common bubbles : a mixed causal non-causal dynamic factor model

This paper introduces a novel dynamic factor model designed to capture common locally explosive episodes, also known as common bubbles, within large-dimensional, potentially non-stationary time series. The model leverages a lower-dimensional set of factors exhibiting locally explosive behavior to identify common extreme events. Modeling these explosive behaviors allows to predict systemic risk and test for the emergence of common bubbles. The dynamics of the explosive factors are modeled using mixed causal non-causal models, a class of heavy-tailed autoregressive models that allow processes to depend on their future values through a lead polynomial. The paper establishes the asymptotic properties of the model and provides sufficient conditions for consistency of the estimated factors and parameters. A Monte Carlo simulation confirms the good finite sample properties of the estimator, while an empirical analysis highlights its practical effectiveness. Specifically, the model accurately identifies the common explosive component in monthly stock prices of NASDAQ-listed energy companies during the financial crisis in 2008 and predicts its evolution significantly outperforming alternative forecasting methods. This new approach offers a powerful tool for detecting common bubbles and predicting their evolution, providing relevant insights for policymakers and investors.