Forecasting Global Volatility with Predictive Spillover Networks: A Neuro-Econometric Spatio-Temporal Transformer for Asynchronous Financial Markets

Abstract

Forecasting global realized volatility requires a model that can learn from interconnected markets without treating zero-coded exchange closures as observed zero volatility. We develop PGA-Trans-HAR, a neuro-econometric architecture that combines a rolling ridge-VAR/GFEVD predictive-connectedness network, masked spatio-temporal attention, and a frozen HAR anchor. Missing observations used to estimate the rolling econometric prior are completed only within the trailing information set available at the forecast origin. An asymmetric source mask prevents closed markets from transmitting zero-coded closure signals. A learned, market-specific gate allocates weight between the econometric prior and data-driven spatial attention. A bounded inverse-softplus correction then refines the HAR forecast while preserving positivity. We evaluate eight international equity indices from 2006 to 2022 at 1-, 5-, and 22-union-calendar-day forecast leads, where the target is the one-day realized volatility observed at the corresponding future date. The design uses five-seed ensembles, select-and-refit estimation, structural ablations, HAC-adjusted Diebold--Mariano tests, and block-bootstrap Model Confidence Sets. PGA-Trans-HAR records the lowest cross-market average MAE at the 1-day forecast lead and the lowest average MSE and MAE at the 5- and 22-union-calendar-day forecast leads. Relative to HAR, both losses decline for all eight markets at the 1- and 5-day forecast leads and for seven markets at the 22-day forecast lead. The evidence shows that combining an origin-aligned econometric network with masked attention can improve multi-market volatility forecasts in asynchronous financial environments.