A Measure of Variability in Co-movement for Economic variables: a time-varying coherence function approach. Gate working paper 08/27

In this article, we suggest testing the instability of the co-movement processes in time and frequency for the GDP growth rate series by the frequency approach, which bases essentially on the evolutionary spectral analysis (Priestley, 1965-1996). We propose a new measure of dynamic co-movement between two time series. The graphic analysis of the Time-Varying Coherence Function (TVCF) reports the existence of variability in dynamic correlation between the two series. Our goal is to test firstly stability in both spectral density for the two series and the cross-spectra density, then we detect various points of changes in TVCF. The two approaches used to know possible fact that influence the synchronisation process. For the break points estimation in the last series we use the algorithm provided by Bai and Perron [1998, Computation and analysis of multiple structural change models, Journal of Applied Econometrics 18, 1-22]. The two tests detects endogenously structural change date. It reports the occurrence of the dates of break