High-dimensional penalized arch processes

We introduce a general methodology to consistently estimate multidimensional ARCH models equation-by-equation, possibly with a very large number of parameters through penalization (Sparse Group Lasso). Some families of multidimensional ARCH models are proposed to tackle homogeneous or heterogeneous portfolios of assets. The corresponding conditions of stationarity and of positive definiteness are studied. We evaluate the relevance of such a strategy by simulation. The relative forecasting performances of our models are compared through the management of financial portfolios.