Tensor graphical Lasso for cryptocurrency portfolio analytics

Abstract Recent failures of major cryptocurrency exchanges and widespread crypto scams highlight the urgent need for stronger regulatory oversight. Meanwhile, tensor-based frameworks are increasingly used to model complex interdependencies across crypto-trading platforms. A key challenge is reliably estimating precision matrices for tensor-valued processes, which can uncover hidden connections and risk propagation between exchanges, including undisclosed trading relationships and cross-platform exposures and systemic financial risks overall. However, most existing tensor precision matrix estimations assume independence, failing to account for the temporal dependencies that characterize crypto-markets. This limitation proved particularly damaging in events such as the FTX collapse, where interconnected trading activities and hidden leverage generated rapid systemic risk across platforms. To address this gap, we propose WeDTLasso, a novel graphical model for estimating precision matrices of temporally dependent tensor-valued data, able to capture how risks propagate through crypto-exchange networks over time. We derive theoretical guarantees in the form of non-asymptotic near-oracle error bounds and demonstrate WeDTLasso's value for regulatory oversight by analysing cross-platform risk transmission in cryptocurrency markets. Our results show that accounting for temporal dependencies is essential for identifying systemic risks and market manipulation and can deliver up to 50% improvements in Sharpe ratios for portfolio construction compared to existing methods.