Estimating rational stock-market bubbles with sequential Monte Carlo methods

Rotermann Benedikt; Wilfling Bernd

Abstract
Considering the present-value stock-price model, we propose a new rational parametric bubble specification that is able to generate periodically recurring and stochastically deflating trajectories. Our bubble model is empirically more plausible than its predecessor variants and has neatly interpretable parameters. We transform our entire stock-price-bubble framework into a nonlinear state-space form and implement a fully-fledged estimation framework based on sequential Monte Carlo methods. This particle-filtering approach, originally stemming from the engineering literature, enables us (a) to obtain accurate parameter estimates, and (b) to reveal the (unobservable) trajectories of arbitrary rational bubble specifications. We fit our new bubble process to artificial and real-world data and demonstrate how to use parameter estimates to compare important characteristics of historical bubbles having emerged in different stock-markets with each other.

Keywords
Present-value model; rational bubble; nonlinear state-space model; particle-; filter estimation; EM algorithm