Time-frequency analysis of crude oil and S&P500 futures contracts

We use frequency-domain techniques, namely wavelets and cross-spectra, to examine the association between the daily prices of crude oil futures and daily S&P500 futures closing prices over the past several decades. We investigate contemporaneous and lag--lead relationships in levels and returns. It is our belief that the wavelet and cross-spectral analyses employed in this paper offer insights regarding the relationship between oil prices and stock returns that are not apparent from a conventional time-domain framework. Our findings cast doubt on the purported negative relationship between oil and the U.S. stock market. Our analysis suggests that oil prices lead oil volume, and S&P500 trading volume leads S&P500 prices.