Most transition-finance assets (green bonds, EU emission allowances, clean-energy equities) have only a few years of daily data and virtually no intraday history, rendering standard spillover tools either infeasible (high-dimensional MGARCH) or inapplicable (realized-variance VARs). We develop an Adaptive-Lasso MGARCH (AL-MGARCH) estimator that applies an L1 penalty with adaptive weights to shrink negligible cross-effects to zero, reducing the active parameter set from O(N2 ) to O(N) while retaining oracle-selection properties. We also generalise Diebold-Yilmaz-style connectedness to daily returns, enabling single-step monitoring of transition-risk networks when intraday data are unavailable. Using eight daily series (2018-2025), we document a bond-centred volatility regime before 2022 and a natural-gas- and coal-centred regime after the Russia-Ukraine shock, reconciling mixed evidence on whether green assets hedge or amplify systemic risk.