(also taken from FRED), whose monthly series is derived as the standard deviation of the daily returns in each month in the sample. Motivated by the aforementioned studies about the possible effects of real interest rates and stock market uncertainty on the co-movement of commodity price returns, we regress the monthly series of estimated rolling absolute correlations between the price returns of commodities _x_ and _z_ – with _x_ = _z_ and _x, z_ = 1 _, ...,_ 11 – on the annualized real interest rate and the standard deviation of S&P500 stock price returns. Specifically, we study the statistical properties of the model � where<sup>�</sup> _ρxz,w,t_ is the estimated value of the rolling correlation between commodities _x_ and _z_ at time _t_ and _w_ is the length of the window used to compute the rolling correlations, i.e. _w_ = 24 months, in this case; _L_ = 12 is the maximum lag determined using the Schwarz criterion; _RRt_ is the real interest rate and _σSP_ 500 is the standard deviation of S&P500 returns. A Newey-West correction, based on a Bartlett kernel and a fixed bandwidth, is employed to produce reliable standard errors for the regression coefficients. The dependent variable in the regression is measured in absolute value to measure whether returns on safe assets (the real interest rates) and/or the volatility of stock markets (market uncertainty) are statistically associated with the degree of co-movement in commodity price returns, regardless of its sign.<sup>14</sup> Table 3 reports the coefficients associated with the two regressors from the model estimated on the full sample. Table 7 in Appendix B reports the coefficients estimated from the regressions run on the four different subsamples previously identified in Section 2.

Unlike Byrne, Fazio and Fiess (2013), we fail to find a statistically significant association between the real interest rate and the co-movement of commodity price returns over the full sample of data. In particular, out of 55 real interest rate coefficients estimated in 55 linear models, only 2 are statistically significant and negative as predicted by theoretical arguments. However, there seems to be some (limited) time-variation in such association from a statistical point of view. From the regression analysis run on the four subsamples, we observe statistically negative coefficients in a few cases (10 and 8) during the first two subperiods, especially when the dependent variable is the time-varying correlation between price returns of energy commodities and some agricultural commodities. Over the subsequent two subperiods, the number of statistically negative coefficients shrinks to 2 and 3. A possible explanation for this finding is that Byrne, Fazio and Fiess (2013) base their analysis on annual data spanning the 1900-2008 period of time, while we work with monthly data over a shorter period of time. The impact of macroeconomic conditions on the comovement of commodity price returns might be more easily detectable when considering long time spans. On the other hand, a statistically positive link between the standard deviation of S&P500 stock price returns and the co-movement of commodity price returns is much more evident. Over

> 14Qualitatively similar results are found when the dependent variable of the regression is the signed rolling correlation series (i.e., without absolute values), given that most of the derived pairwise rolling correlations are positive.

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