Oil and the stock market revisited: A mixed functional VAR approach

This paper proposes a new mixed vector autoregression (MVAR) model to examine the relationship between aggregate time series and functional variables in a multivariate setting. The model facilitates a reexamination of the oil‐stock price nexus by estimating the effects of demand and supply shocks from the global market for crude oil on the entire distribution of U.S. stock returns since the late 1980s. We show that the MVAR effectively extracts information from the returns distribution that is more relevant for understanding the oil‐stock price nexus beyond simply looking at the first few moments. Using novel functional impulse response functions (FIRFs), we find that oil market demand shocks tend to increase returns, while both demand and supply shocks reduce volatility, and have an asymmetric effect on the returns distribution as a whole. In a value‐at‐risk (VaR) analysis, we also find that the oil market contains important information that reduces expected loss, and that the response of VaR to the oil market demand and supply shocks has changed over time.