Time-varying spillover of multi-scale positive and negative bubbles in stock and oil markets

• TVP-VAR spillover between oil and stock bubbles analyzed. • MS-LPPLS-CIs detect positive and negative bubbles in the short-, medium and long-term • Negative bubble spillovers are significantly stronger and more directional • U.S. equity market is the transmitter to the oil market post-2008 • Spillover effects most pronounced at short- and medium-term horizons The objective of this paper is to analyze time-varying spillover between bubbles in oil and stock markets of the U.S. In this regard, we first use the Multi-Scale Log-Periodic Power Law Singularity Confidence Indicator (MS-LPPLS-CI) approach to detect both positive and negative bubbles in the short-, medium and long-term in the two markets. In the second-step, we utilize a Time-Varying Parameter Vector Autoregressive (TVP-VAR) model to conduct the spillover analysis among the indexes of oil and stock positive and negative bubbles. Based on data covering the monthly period of January 1999 to June 2025, we find that negative bubble spillovers are significantly stronger and more directional than positive ones, with the U.S. equity market emerging as the transmitter to the oil market post-2008. This represents a structural shift from the traditional oil-to-equity transmission paradigm. Moreover, spillover effects are most pronounced at short- and medium-term horizons, intensifying during crisis periods. Our findings suggest that oil is increasingly behaving as a financial asset rather than a physical commodity, with important implications for portfolio diversification and risk management.