Sparse multivariate GARCH

We propose sparse versions of multivariate GARCH models that allow for volatility and correlation spillover effects across assets. The proposed models are generalizations of existing diagonal DCC and BEKK models, yet they remain estimable for high-dimensional systems of asset returns. To cope with the high dimensionality of the model parameter spaces, we employ the L1 regularization technique to penalize the off-diagonal elements of the coefficient matrices. A simulation experiment for the sparse DCC model shows that the true underlying sparse parameter structure can be uncovered reasonably well. In an application to weekly and daily market returns for 24 countries using data from 1994 to 2014, we find that the sparse DCC model outperforms the standard DCC and the diagonal DCC models in and out of sample. Likewise, the sparse BEKK model outperforms the diagonal BEKK model.