Our colloquium speaker for this Thursday is Professor Pierluigi Vellucci from Dept. of Economics, Roma Tre University, Italy. 

Fourier analysis is one of the commonly used methods to analyse periodicity in the frequency domain. In particular, Fourier transform (FT) uses sine and cosine functions to reconstruct a signal or a time series and gives information about their global frequency distribution. Since time information is not considered, FT is most suitable for  time series that are generated by time-invariant systems. The loss of time information makes it difficult to identify both transient relations and structural changes and discontinuities in the series under study. This drawback is overcome by wavelet analysis, since the continuous wavelet transform (CWT) preserves both time and frequency information by decomposing the original time series  into a wavelet function parameterised in terms of time location and scale. Then, it is usual to refer to this as a time-frequency analysis.
In this talk, taken from a joint work with Loretta Mastroeni, Greta Quaresima and Alessandro Mazzoccoli,  we show how wavelet analysis approach is able to investigate oil-food price correlation and its determinants in the domains of time and frequency. The wavelet transform decomposes a time series into subsequences at different resolution scales. In particular, it decomposes given data into high and low-frequency components, which correspond, respectively, to short and long run dynamics.
We show that oil-food price co-movement is only apparent. Indeed, most of the comovements are due to the activity of commodity index investments. (Here the word “comovement” means a phenomenon of a time series “moving with” another one.) Moreover, the activity of commodity index investments gives evidence of the overall financialisation process, i.e. the recent phenomenon involving an unprecedented inflow of institutional funds into commodity futures markets.
In addition, we employ wavelet entropy to assess the predictability of the time series under consideration at different frequencies. We also introduce a novel measure, the Cross Wavelet Energy Entropy Measure (CWEEM), based on wavelet transformation and information entropy, with the aim of quantifying the intrinsic predictability of food and oil given demand from emerging economies, commodity index investments, financial stress, and global economic activity. The results show that these dynamics are best predicted by global economic activity at all frequencies and by demand from emerging economies and commodity index investments at high frequencies only.