Identifying economic cycles in Spain using wavelet functions: oil price, industrial production and consumer price indices

Abstract

This paper analyses the economic cycles in Spain over a long period of time according to available data by using three related variables: Oil Price (1946M1-2015M9), Industrial Production Index (1993M2-2015M9) and Consumer Price Index (1961M1-2015M9). The impact of shocks on oil price has been the subject of an extensive study, although modelling their effects is not a trivial undertaking. Our contribution focuses on applying the Morlet Wavelets to identify the presence of unstable cycles in data series by calculating the Wavelet Power Spectrum with the MATLAB software. Moreover, some bivariate techniques are applied to display the mutual influence of the Oil Price with the Industrial Production Index and the Consumer Price Index. The Cross Wavelet Coherency and the relationship among phases can also be used to detect co-movements and potential causality relationships in frequency bands over time. Finally, by studying these variables we can draw certain comparative conclusions with the US and German economies, whose corresponding variables have been considered by other authors using this same tool.