industry.

# **3.3 Rolling Unconditional Correlations and Determinants**

With the objective of understanding if there are factors driving the co-movement under investigation, we adopt a flexible approach to compute rolling unconditional correlations between commodity nominal price returns based on Tang and Xiong (2012).<sup>13</sup> We only report and discuss results related to rolling correlations estimated using a 24-month rolling window. Our empirical results are robust to alternative rolling windows. For example, a fixed rolling window of 60 monthly observations is also used for comparison purposes. Further details are available upon request.

Similar to the dynamic conditional correlations obtained from the estimation of the DCC model and discussed in the previous section, we focus on the unconditional correlations between maize and soybean oil price returns (here used again as reference commodities) and the returns of all other commodities. The estimated unconditional correlations are plotted in Figures 6 and 7 in Appendix B. These rolling correlations exhibit fluctuations similar to those observed in the evolution of the dynamic conditional correlations.

Real interest rates and stock market uncertainty might, in principle, affect the co-movement of commodity price returns. Some of the reasons can be found, for example, in the work of Frankel (2008), Gruber and Vigfusson (2012) and Byrne, Fazio and Fiess (2013). They argue that the correlations of commodity price returns should be inversely related to the real interest rate. The theoretical foundations of this claim can also be found in Deaton and Laroque (1992, 1996) and are based on the idea that a fall in the interest rate lowers the volatility of prices (smoothing transitory shocks through lower inventory costs) and increases the correlations of price returns if covariant shocks are more persistent than idiosyncratic shocks. Byrne, Fazio and Fiess (2013) argue that the standard deviation of stock market prices can be used as a proxy of market uncertainty, in line with Beck (1993) and Dixit and Pindyck (1994)’s suggestion that market risk and uncertainty might be associated with movements in commodity prices. According to Beck (1993), uncertainty may have a positive effect on commodity prices because volatile commodity prices are likely to reduce inventories and, consequently, their price. Dixit and Pindyck (1994) predict a negative effect of uncertainty on commodity prices as uncertainty increases the option value of waiting (since investment in the production of primary commodities may be irreversible). Gilbert (2010) also suggests that co-movements across commodity prices can be better explained by macroeconomic and financial conditions than by market-specific factors.

In this study we consider two possible determinants of the co-movement of commodity price returns: (i) a real interest rate series computed as the difference between an annualized 3-month Treasury bill interest rate series obtained from the Board of Governors of the Federal Reserve System and a series of annual inflation rates calculated from a monthly non-seasonally adjusted consumer price index series taken from the Federal Reserve Bank of St Louis Economic Dataset (FRED); and (ii) the standard deviation of Standard & Poor’s 500 (S&P500) stock price returns

> 13The technical details are presented in Section A.4.

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