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.

We studied the problem of forecasting full future realized–variance (FRV) paths $y_{t,1:H}$ over $H=30$ trading days. We proposed a depth–weighted ridge (DW–ridge) estimator that (ⅰ) enforces the natural monotonicity of cumulative variance via a pool–adjacent violators post–projection and (ⅱ) adapts to market regimes through observation weights derived from a Wasserstein–based curve depth. At the daily frequency, we took squared returns as a practical realized–variance proxy, so that the FRV path is the cumulative sum of next–day squares. Empirically, we used daily data for two liquid U.S. exchange-traded funds (ETFs; XLE and SLV) and two major cryptocurrencies (BTC–USD and ETH–USD) from January 1, 2020, to December 31, 2024, under a 60%/20%/20% train–calibration–test split. On the ETF benchmarks, DW–ridge improved all–horizon pathwise root mean squared error (RMSE) by about 3.1% (XLE) and 2.8% (SLV) relative to a monotone ridge baseline, with statistically significant short–horizon (H1–3/H1–5) mean squared error (MSE) gains under a moving–block bootstrap. On BTC–USD and ETH–USD, all–horizon RMSE reductions were around 6.0% and 6.5%, respectively. A block–conformal diagnostic based on depth–derived nonconformity scores attained near–nominal or conservative coverage on test blocks, so sharper forecasts were not obtained at the expense of reliability. Overall, depth reweighting provided a simple, fast, and empirically effective enhancement to monotone FRV path forecasting across both sector ETFs and major cryptocurrencies.