Globalisation and financial liberalisation have made financial markets more correlated and connected. In this context, it has become extremely important to understand the connectedness and correlation among different financial markets and commodities. This paper attempts to extend applicable empirical studies by examining the connectedness between volatilities of commodity convenience yields and zero-coupon inflation swap rates. We conduct our study by using both the spillover index methodology provided by Diebold and Yilmaz (2009,2012) as well as Barunik and Krehlik's (2018) methodology to decompose the index to its frequencies for short-, medium and long-term dynamics. Although, empirical results based on Diebold and Yilmaz's (2012) methodology show that high total connectedness exists between the variables for the whole time period, our results based on Barunik and Krehlik's (2018) approach shows that this connectedness exists only in the long-term. The results also indicate that the connectedness dynamics change when the effect of cross-correlations is considered.