Stochastic coefficient GARCH-X models: evidence from the US and ASEAN-5 equity markets

This artcle introduces the Stochastic Coefficient GARCH-X (SC-GARCH-X) model, extending the standard GARCH-X framework by allowing conditional variance parameters to vary over time as a stochastic process driven by exogenous variables. We establish stationarity conditions and discuss the asymptotic properties of the Quasi-Maximum Likelihood (QML) estimator, confirming its reliability via Monte Carlo simulations. Empirical applications to US and ASEAN-5 equity markets using range-based volatility show that SC-GARCH-X provides a superior fit and forecasts for developed markets. Conversely, simpler asymmetric GARCH models better characterize certain emerging markets, indicating that volatility dynamics vary across market development stages.