Exuberant increases in the price of certain goods or financial assets, far beyond what could appear to be a reasonable intrinsic value, are commonly designated as “bubbles”. Such phenomena are not new: the Tulip Mania of the 17th century and the South Sea bubble of 18th century, for instance, are well documented historical instances of such events. Sharp reversals, or “crashes”, systematically follow the exuberant increasing phase of bubbles and have dramatic impact on the broader economy and society. The United States housing bubble, which peaked in 2006, was the trigger for a global economic crisis which required unprecedented intervention by states and central banks across the world.
Monitoring and forecasting the evolution of asset prices, especially the ones undergoing rapid increases, could provide the ability for financial regulators to steer the markets away from overheating, avoiding sharp collapses or allowing to contain their impact. Forecasting bubbles and their crashes remains however an open research question.
A recent modelling approach at the intersection of time series econometrics, statistics and probability theory -so-called “anticipative” or “noncausal” time series models- is very promising in that regard as it allows to fit and reproduce adequately the observable and statistical characteristic of bubbles across a wide range of financial indexes, stocks, commodities, cryptocurrencies and economic indicators. A blind spot of this non-standard modelling approach is that no theory exists regarding forecasting the future evolution of bubbles or the incoming occurrence of a crash. The objective of this project is precisely to provide such theoretical results which will enable the use of anticipative time series models for forecasting bubble crashes.
