Multivariate volatility forecasting across international equity markets presents a fundamental information-set problem: asynchronous exchange closures dictate which market observations belong to the information filtration at any forecast origin. We investigate whether regularized, origin-admissible cross-market information yields incremental accuracy beyond established benchmarks. We develop PGA-Trans-HAR, combining an origin-admissible ridge-VAR/GFEVD connectedness prior with spatial self-attention. A time-invariant market gate governs their allocation, asymmetric attention masking prevents closed exchanges from transmitting spurious signals, and a direct-horizon HAR baseline anchors residual corrections. Using high-frequency data from eight major indices (2006--2022), we evaluate direct forecasts at 1-, 5-, and 22-day horizons across all-days and common-days panels, five-seed ensembles, structural ablations, HAC-adjusted Diebold--Mariano tests, and Model Confidence Sets. Relative to univariate HAR, the framework reduces MSE and MAE across all markets at daily and weekly horizons, and seven of eight monthly. Among linear and deep learning benchmarks, it achieves the lowest daily average MAE and the lowest weekly/monthly average MSE and MAE. Structural ablations show that spatial restrictions are essential: learned market gates improve accuracy over uniform weighting at medium-to-long horizons, while daily forecasts favor stronger scalar shrinkage. Disciplined, origin-aligned cross-market information yields genuine predictive gains, especially at medium and long horizons where structural spillovers persist.

翻译：暂无翻译