Stock market bubbles and the realized volatility of oil price returns

Using monthly data for the G7 countries from 1973 to 2020, we study whether stock market bubbles help to forecast out-of-sample the realized volatility of oil price returns. We use the Multi-Scale Log-Periodic Power Law Singularity Confidence Indicator (MS-LPPLS-CI) approach to identify both positive and negative bubbles in the short-, medium, and long-term. First, we successfully detect major crashes and rallies using the MS-LPPLSCIs. Having established the relevance of the bubbles indicators, and given the large number of them, we use widely-studied shrinkage (Lasso, elastic net, ridge regression) approaches to estimate our forecasting models. We find that stock market bubbles have predictive value for realized volatility at a short to intermediate forecast horizon. The number of bubble predictors included in the penalized forecasting models tend to increase in the forecast horizon. We obtain our main finding for the various types of stock market bubbles, and for good and bad realized volatilities.