International volatility forecasting requires models to combine persistent local dynamics with information observed across different trading calendars. We propose PGA-Trans-HAR, an attention model that learns a bounded correction to a frozen heterogeneous autoregressive (HAR) forecast. A rolling predictive-connectedness graph guides spatial attention, while source masks accommodate market closures on the union calendar. We evaluate daily range-based volatility for eight equity indices from March 2013 to September 2026 at leads of 1, 5, and 22 union-calendar dates. Among seven primary forecasting models, PGA-Trans-HAR achieves the lowest equal-market average MSE at the 1- and 22-date leads and the lowest average QLIKE at all three leads. Its MSE reductions relative to HAR are 1.70% and 1.13% at the two endpoints. At the 1-date lead, the standard deviation of MSE across five fitted seeds is 0.00057, compared with 0.01260 for DCRNN-HAR and 0.03727 for GNN-HAR. The model is retained in 47 of 48 market-horizon MSE cells in the 90% Model Confidence Sets across two evaluation panels. Under historical-tail calibration, joint VaR/ES scores improve on HAR at the 1- and 5-date leads. A common intraday exposure rule yields annual CER gains of 7.89 to 9.28 basis points relative to HAR across the specified cost scenarios. These results support bounded correction of a local econometric forecast as a design for accurate and stable cross-market volatility prediction.

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