In this work we propose a forecasting methodology suitable for large panels of liquidity measures based on exploiting the cross-sectional commonality structure of volume. We begin by providing a number of stylized facts for a panel comprising the CAC40 constituents.  We document the presence of a strong common component that is correlated with market volatility. Moreover, after the common component is filtered out, we find evidence of dependence across a number of ticker pairs. These stylized facts motivate us to propose a hybrid forecasting model that is made up of a factor and sparse vector-autoregressive components. We estimate such a model by combining PCA (Principal Component Analysis) and LASSO (Least Absolute Shrinkage and Selection Operator) estimation. We apply our methodology to forecast the intra-daily liquidity of the CAC40 constituents across different intra-daily frequencies. Results show that our approach systematically improves forecasting accuracy over a number of univariate and multivariate benchmarks.