Revisiting the spanning hypothesis with machine learning methods: a systematic literature review

The spanning hypothesis in government bond markets posits that a small number of yield-curve factors fully summarize the information relevant for pricing and forecasting bond returns. Despite extensive empirical investigation, evidence on the validity of this hypothesis remains mixed. Concurrently, recent advances in machine learning have renewed interest in uncovering nonlinear predictive relationships between macroeconomic conditions and the term structure of interest rates. This paper provides a systematic literature review of studies that employ machine learning methods to forecast bond yields and excess returns, with a particular focus on their implications for the spanning hypothesis. We synthesize evidence across datasets, model classes, validation strategies, and approaches to economic interpretation. The literature is highly fragmented, lacking a coherent model hierarchy or standardized out-of-sample evaluation framework. Nonetheless, evidence from methodologically rigorous studies suggests that nonlinear methods, in particular parsimonious neural networks and tree-based ensembles, can extract predictive signals from macroeconomic data that are not spanned by conventional yield-curve factors. At the same time, we document that reported forecasting gains are frequently overstated due to methodological shortcomings, including inappropriate evaluation metrics, look-ahead bias arising from revised macroeconomic data, and data leakage induced by global pre-processing and model selection. Taken together, our findings imply that while the true predictive advantage of machine learning over traditional term-structure benchmarks is more modest than often claimed, it remains economically meaningful. We conclude that future progress in macro-finance forecasting will likely depend less on increasingly complex algorithms and more on the standardization of validation practices and data handling conventions. Interpretable “gray-box” models that combine nonlinear flexibility with economic structure appear particularly promising in the context of the spanning hypothesis, as they offer a pragmatic compromise between forecasting performance and the transparency required for asset pricing, portfolio allocation, and policy analysis.