@article{SÖZEN2026, 
author = {Çağlar SÖZEN and Onur ŞEYRANLIOĞLU and Arif ÇİLEK and Abdulmuttalip PİLATİN},
title = {Monotone functional regression with hybrid depth weighting and block-conformal prediction bands for forward realized variance paths},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {6},
pages = {18525-18552},
keywords = {forward realized variance, functional regression, depth weighting, isotonic projection, block-conformal prediction, liquid exchange-traded funds},
url = {https://www.sciopen.com/article/10.3934/math.2026753},
doi = {10.3934/math.2026753},
abstract = {We forecast forward realized variance (FRV) paths, defined as cumulative future daily variance proxy curves over a finite trading horizon, using a leakage-disciplined functional framework for multiday risk assessment. The framework combines multiresponse ridge regression, hybrid depth weighting, horizon-weighted blocked cross-validation, and isotonic post-projection to preserve the monotone structure of FRV paths. Uncertainty is summarized through upper one-sided block-calibrated conformal bands, interpreted as empirical risk envelopes under temporal dependence rather than exact distribution-free guarantees. In a fixed panel design for four liquid exchange-traded funds, GDX, GDXJ, XLE, and UUP, over the period 2010–2025, the proposed model reduces long-horizon mean squared error relative to rolling historical FRV by approximately 31.8%, 20.4%, 36.5%, and 28.0%, respectively, over    h  =  20      :    30. Comparisons with heterogeneous autoregressive (HAR) ridge and functional principal component autoregressive (FPCA-AR) benchmarks are asset-dependent. The proposed model is most favorable for GDX and remains close to HAR ridge for GDXJ, whereas HAR ridge and FPCA-AR remain competitive for XLE and UUP. Coverage is conservative or close to nominal at    α  =  0.05 but more heterogeneous at    α  =  0.10. Robustness checks support a cautious interpretation of the method as a shape-aware enhancement of rolling FRV forecasting.}
}