Smooth volatility shifts and spillovers in U.S. crude oil and corn futures markets

• Trigonometric terms can be used to detect structural change in volatility.
• Controlling for structural change using trigonometric terms can reduce model persistence.
• There are structural breaks in the volatility of corn and crude oil futures.
• Term structure of corn and crude oil futures volatility changes over time.
• Volatility in corn and crude oil futures markets is less persistent than a standard GARCH model might indicate.

Recent developments in biofuel technologies have resulted in heightened linkages between the petroleum and agricultural sectors. As such, a large price and/or volatility shift experienced in one sector is now more likely to spill-over into the other. In trying to capture the interrelations present in the two markets, we take seriously the importance of properly modeling smooth structural shifts. We incorporate trigonometric functions into a multivariate GARCH model of crude and corn futures prices in order to obtain the empirical volatility response functions and the time-varying correlation coefficient. Although both short-term and long-term futures exhibit shifts in the mean and volatility, volatility shifts do not manifest themselves in the same manner for different maturities. This indicates that the term structure of futures volatility changes over time.