We introduce LASSO-type regularization for large-dimensional realized covariance estimators of log-prices. The procedure consists of shrinking the off-diagonal entries of the inverse realized covariance matrix towards zero. This technique produces covariance estimators that are positive definite and with a sparse inverse. We name the estimator realized network, since estimating a sparse inverse realized covariance matrix is equivalent to detecting the partial correlation network structure of the daily log-prices. The large sample consistency and selection properties of the estimator are established. An application to a panel of US blue chip stocks shows the advantages of the estimator for out-of-sample GMV asset allocation.
