Detection of lead-lag relationships using both time domain and time-frequency domain: An application to wealth-to-income ratio

The objective of this paper is the joint application of two different methodological concepts for the detection of lead-lag relationships in economic time-series in order to investigate their consistency and their potential complementarity. The first methodology, a time domain analysis based on vector error correction model, provides evidence about the existence of long-run equilibrium of the time-series and the short-run lead-lag behaviors. The second methodology, a time-frequency concept based on the phase difference of the cross-wavelet coherence, analyzes the lead-lag relationships across various timescales and reveals the altering of leadership over time. The two methods are applied to time-series of wealth-to-income ratio of four developed countries over the period 1970-2010 and analyze the lead-lag relationships of the countries in the long-run and in the short-run. The results show that the two methods are consistent in their major long-run findings, however, they reveal different aspects regarding the short-run dynamics of the lead-lag relationships. Furthermore, the results suggest the complementarity of the two methodologies in the context of a complete framework for the analysis of the lead-lag relationships in non-stationary economic time-series.