and falls in the price of energy, metals and foods is unlikely to be coincidental and may be the result of a common set of macroeconomic and financial factors driving prices across a wide range of commodities. Byrne, Fazio and Fiess (2013) document a significant degree of price co-movement across 24 commodities and argue that such co-movement may be due to a common factor related to macroeconomic fundamentals, such as the real interest rate and stock market uncertainty.

In this paper we adopt a multivariate approach to comprehensively examine the degree of co-movement among major commodity markets. We first study the extent of cross-section correlation and the time-varying pairwise unconditional and conditional correlations between 11 energy, agricultural and food price returns using monthly data from January 1970 through May 2013. Specifically, we use the uniform spacings method developed by Ng (2006) to test for the presence and evaluate the extent of unconditional co-movement in commodity price returns. We estimate a multivariate dynamic conditional correlation (DCC) model, based on Sheppard and Engle (2001) and Engle (2002), to analyze the time-varying conditional correlations between commodity price returns. Furthermore, we investigate whether bivariate rolling unconditional correlations between commodity price returns are statistically associated with specific macroeconomic and financial factors by means of a linear regression analysis.

We contribute to the existing empirical literature on the topic along several dimensions. First, contrary to most previous studies, which mainly examine the co-movement of commodity price returns, we model the evolution over time of the interlinkages between markets by also allowing for time-variation in price-specific conditional volatilities.<sup>3</sup> Allowing for time-variation in mixed and non-mixed conditional second moments permits a more accurate assessment of the dynamic relationships between markets (Gallagher and Twomey, 1998). Second, our investigation is restricted to major energy, agricultural and food commodities. The goal is to analyze the extent of price correlations both within and across energy- and food-related markets. Agricultural commodities, for example, are expected to be correlated because they are generally close substitutes in demand, have similar input costs and share common market information. Yet, growing financial market integration and the development of agricultural futures markets might have corroborated these interdependencies in recent years. Furthermore, the interlinkages between energy and agricultural markets, typically related through production and transportation costs, may have become stronger due to the recent development of the biofuel industry and the increasing demand for agricultural produce in the production of ethanol and biodiesel (Rajagopal and Silverman, 2007). Our period of analysis is sufficiently large to allow a characterization of the evolution of commodity prices in terms of trends and structural changes, which could be associated with particular events in the commodity markets (see Figure 1). The use of monthly data allows us to capture dynamics that would otherwise be hidden in lower frequency data.<sup>4</sup> Finally, motivated by the work of Frankel

> 3Deb, Trivedi and Varangis (1996), Zhao and Goodwin (2011) and Gardebroek, Hernandez and Robles (2013) are among the few studies that focus on market interactions in terms of conditional second moments. The authors of these studies estimate BEKK models following Engle and Kroner (1995). Deb, Trivedi and Varangis (1996) analyze excess co-movement across apparently unrelated commodities using a likelihood ratio test; the other two studies examine volatility spillovers between major agricultural commodities.

> 4At the same time, we avoid higher frequency data, which could instead be characterized by a high noise-to-signal

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