Wavelet-domain elastic net for clustering of volatilities

Abstract

We show that the non-decimated wavelet transform and the elastic net can be used to improve clustering of volatilities. The non-decimated wavelet transform of a time series breaks up the series into a number of details levels and a single smooth level. The elastic net simultaneous does automatic variable selection and continuous shrinkage, and it can select groups of correlated variables. The methodology is applied to the daily stock market indexes. The non-decimated wavelet transform details coecients are modeled with the ARMA-GARCH process level wise. The cluster analysis obtained by the elastic net shows that our methodology agree with the results observed on the literature.