Time-Localized Wavelet Multiple Regression and Correlation : Eurozone Stock Markets Across Scales and Time

This paper extends wavelet methodology to handle co-movement dynamics of multivariate time series via moving weighted regression on wavelet coefficients. The concept of wavelet local multiple correlation is used to produce one single set of multi-scale correlations along time, in contrast with the large number of wavelet correlation maps that need to be compared when using standard pairwise wavelet correlations with rolling windows. Also, the spectral properties of weight functions are investigated and it is argued that some common time windows, such as the usual rectangular rolling window, are not satisfactory on these grounds.The method is illustrated with a multi-scale analysis of the co-movements of Eurozone stock markets during this century. It is shown how the evolution of the correlation structure in these markets has been far from homogeneous both along time and across timescales featuring an acute divide across timescales at about the quarterly scale. At longer scales, evidence from the long-term correlation structure can be interpreted as stable perfect integration among Euro stock markets. On the other hand, at intramonth and intraweek scales, the short-term correlation structure has been clearly evolving along time, experiencing a sharp increase during financial crises which may be interpreted as evidence of financial ‘contagion'