Distribution-free uncertainty quantification for daily treasury yield curves with functional principal component forecasting and vector autoregression

We investigated one-step-ahead daily U.S. Treasury yield-curve forecasting and provided distribution-free uncertainty quantification for the entire term structure. Using constant-maturity yields from the Federal Reserve Bank of St. Louis (FRED), we first transformed the discrete maturity panel into a dense common maturity grid through a knot-consistent ridge-regularized cubic B-spline smoother, enabling coherent curve-level evaluation. For point prediction, we modeled the yield curve as a functional time series and forecasted functional principal component (FPCA) scores with a vector autoregression (VAR). We benchmarked FPCA–VAR against two widely used alternatives: The dynamic Nelson–Siegel (DNS) model and a raw-maturity PCA–VAR (RawPC–VAR) baseline. To quantify predictive uncertainty without imposing parametric distributional assumptions, we constructed rolling studentized conformal prediction bands using a simultaneous (sup-type) nonconformity score and a moving calibration window; the associated distribution-free validity was taken in the usual conformal (exchangeable) sense and treated as an operational benchmark—rather than a literal time-series guarantee—under temporal dependence. We therefore audited calibration directly on the test block and, to probe regime heterogeneity, implemented an ex-ante Mondrian conformal variant based on a curve-shock indicator that partitioned days into HIGH and LOW regimes. Out-of-sample results showed that FPCA–VAR achieved the lowest integrated squared error and yielded substantially tighter predictive bands than DNS, while Mondrian calibration improved interpretability by revealing and partially reducing regime-dependent coverage imbalances.