We model forward realized-volatility (FRV) curves as multivariate functional responses and introduce a simple, auditable estimator—Depth-Weighted Functional Ridge Regression (DW–FRR)—for pathwise volatility prediction. DW–FRR regresses the entire FRV path on HAR-style covariates augmented with asset fixed effects, while weighting training observations by a clipped Fraiman–Muniz functional depth. The estimator admits the closed form \((Z^\top W Z+\lambda I_p)^{-1} Z^\top W Y^\circ \) , which preserves computational efficiency and facilitates transparent inspection of the design, weighting scheme, and fitted coefficients. We develop a concise theoretical analysis covering existence and uniqueness, Lipschitz stability with respect to weight perturbations, a linear-smoother characterization with effective degrees of freedom \(\textrm{df}(\lambda )\) that is monotone and convex in \(\lambda \) , an oracle-type inequality in expectation and with high probability, and consistency under standard ergodic conditions. Empirically, using daily data for the SPDR S&P 500 ETF Trust and U.S. sector ETFs over 2019–2024 under strictly time-respecting blocked and rolling evaluation designs, DW–FRR remains competitive across settings and improves upon unweighted multivariate ridge most clearly under rolling evaluation, where temporal transfer is more demanding. It also compares favorably with simpler pathwise benchmarks, including the mean curve, a naive \(\sqrt{h}\) -curve, and a horizon-wise HAR-ridge alternative. An ablation over the depth exponent \(\gamma \) indicates that moderate weighting provides the best bias–variance trade-off, with \(\gamma =1\) emerging as a robust default. Overall, DW–FRR provides a lightweight, theoretically grounded, and practically useful baseline for forward volatility-curve forecasting in risk monitoring and margining applications.
