Deep Learning Forecasting of the U.S. Aggregate Bond Index

This study looks at the statistical properties and predictability using deep learning methods of the U.S. aggregate bond index in daily observations spanning 2018 to February 2026. We first establish that index levels are extremely persistent and consistent with unitroot behavior (Dickey and Fuller), while log returns are covariance-stationary with weak linear dependence and pronounced volatility clustering characteristic of ARCH-type processes (Engle; Bollerslev). Motivated by the trade-off between stationarity and information retention, we construct a "stationary but maximally persistent" representation via fractional differencing (Granger and Joyeux; Hosking) following the procedure of L\'opez de Prado, and evaluate shorthorizon forecast using two neural paradigms: (i) Multilayer Perceptrons (MLPs) trained on lagged vectors with joint lag-length and hyperparameter tuning (Hornik et al.; Rumelhart et al.); and (ii) Convolutional Neural Networks (CNNs) trained on Gramian Angular Field (GAF) image encodings (Wang and Oates). Empirically, MLPs match the strong naive persistence benchmark on levels, collapse toward near-zero forecasts on returns, and achieve the strongest incremental performance on the fractionally differenced series, where moderate dependence remains but unit-root drift is attenuated. In contrast, CNN-GAF models deliver consistently negative out-of-sample R 2 across all three representations. Overall, the results imply that, for short-horizon forecasting of broad bond indices, the primary determinant of predictive performance is the transformation of the series-its degree of stationarity and memory-rather than architectural complexity. Lag-based models remain competitive under persistence, while GAFbased CNNs are better suited to pattern-based tasks than to persistence-dominated next-step prediction.