Analyzing the time-frequency lead–lag relationship between oil and agricultural commodities

We analyze the time-frequency co-movement of and lead–lag relationship between price indices of oil and 21 agricultural commodities and attempt to identify the leader and follower among the considered price indices for the 1980M1–2017M5 period. The empirical analysis is conducted using four wavelet tools: wavelet coherency, phase-difference, multiple correlation and multiple cross-correlation. The first two tools are used to identify the time-frequency co-movement of and lead–lag relationship between price indices of oil and 21 agricultural commodities, and the third and fourth tools are used to identify the leader and follower among all series of price indices across different scales. Our results on wavelet coherency show a high degree of co-movement at a long-run horizon for the entire period between the price indices of oil and coal, cotton, fishmeal, maize, rice, rubber and wheat. Furthermore, the connection between these commodity markets and the oil market strengthened after 2000, indicating the importance of financial crisis phenomena and geopolitical turbulence. Additional findings show that short-run investors should invest in the beef and swine (pork) markets, as they have very little correlation with the oil markets. The results of multiple correlation and multiple cross-correlation analysis show that the coffee price was leader or follower across all time scales, except wavelet scale 16, where barely was a leader or a follower.