highest levels of volatility during the 1980s and the 1990s, and up to 2007. The returns of the three energy commodities are consistently the most volatile between the end of the 1980s and 2013, with the exception of coal during between 1987 and 2007. All return volatilities (with the exception of natural gas) rise between 2007 and 2013 with respect to the previous twenty-year period.

Turning to the other distributional properties of the data, maize price returns exhibit a distribution with a long left tail, while natural gas returns are the only returns with a symmetric distribution. All other returns have distributions with long right tails and median returns almost always smaller than average returns. A battery of Shapiro-Wilk tests run on the nominal price returns rejects the null hypothesis that the data are normally distributed in all cases. The kurtosis of all price returns is greater than three, as we observe leptokurtic data. Table 1 also reports the p-values from the Ljung-Box autocorrelation tests run on the squared returns. The null hypothesis of no autocorrelation up to 12 lags is mostly rejected at conventional statistical levels, except the cases of crude oil, maize and sorghum.

All these findings are consistent with the presence of nonlinear time-dependency in the series of price returns, maybe due to the existence of time-varying conditional moments. Figure 3 plots the time-evolution of each nominal price return, whose fluctuations and volatility changes over time are apparent. These descriptive results motivate the adoption of specific econometric techniques to characterize the time-varying properties of the second moments of the commodity price returns in the sample. As already mentioned, particular attention is given to the second mixed moments, which are used in this study to measure the co-movement of price returns.

# **3 Measuring the Co-Movement of Commodity Price Returns**

In this section we describe and discuss the main empirical findings of our investigation. We study the co-movement of commodity price returns in three different ways. We assess the extent of their cross-section unconditional correlation over the full sample and four subperiods by means of Ng (2006)’s methodology. We study the time-evolution of their dynamic conditional correlations by estimating a multivariate DCC model on the data, while allowing for time-varying conditional volatilities. Finally, we model the time-evolution of their unconditional correlations using a rolling regression approach based on Tang and Xiong (2012). In this final context, we also run a regression analysis to statistically investigate the association between the unconditional co-movement of price returns and two of its possible determinants. Further details about the econometric techniques can be found in Appendix A.

## **3.1 Cross-Section Unconditional Correlations**

We formally examine the cross-section co-movement of nominal price returns in energy, agricultural and food markets by following the uniform spacings methodology developed by Ng (2006), which tests for the existence and measures the extent of cross-section unconditional correlation in a panel of data where the number of correlated series is unknown _ex ante_ . This econometric approach 5