Wavelet power spectrum and cross-coherency of Spanish economic variables

Abstract

We analyze six relevant economic and financial variables for the period 2000M1–2015M3 in the context of the Spanish economy: a financial index (IBEX35), a commodity (crude oil price in euros), a foreign exchange index (EUR/USD), a bond (Spanish 10-year bond), the Spanish national debt and the consumer price index. The goal of this paper is to analyze the main relationships between them by computing, using a special toolbox in MATLAB, the wavelet power spectrum and the cross-wavelet coherency associated with Morlet wavelets, focusing our interest on the period variable. We decompose the time–frequency effects and improve the interpretation of the results by non-expert users in the theory of wavelets. This yields empirical evidence on instability periods and reveals various changes and breaks in the causality relationships for the data available from recent years. Moreover, we introduce a comparison with Gaussian wavelets and use the MATLAB software suite for computing, taking the scale instead of the period as the reference variable. These same variables were analyzed individually in a previous paper that specifically considered the decomposition of non-stationary monthly rate series in the period 2000M1–2014M12 using Daubechies wavelets db8 to visualize high frequency variance, seasonality and trend.