We propose a shrinkage and selection methodology specifically designed for network inference using high dimensional data through a regularised linear regression model with Spike-and-Slab prior on the parameters. The approach extends the case where the error terms are heteroscedastic, by adding an ARCH-type equation through an approximate Expectation-Maximisation algorithm. The proposed model accounts for two sets of covariates. The first set contains predetermined variables which are not penalised in the model (i.e., the autoregressive component and common factors) while the second set of variables contains all the (lagged) financial institutions in the system, included with a given probability. The financial linkages are expressed in terms of inclusion probabilities resulting in a weighted directed network where the adjacency matrix is built "row by row". In the empirical application, we estimate the network over time using a rolling window approach on 1248 world financial firms (banks, insurances, brokers and other financial services) both active and dead from 29 December 2000 to 6 October 2017 at a weekly frequency. Findings show that over time the shape of the out degree distribution exhibits the typical behavior of financial stress indicators and represents a significant predictor of market returns at the first lag (one week) and the fourth lag (one month).