Stratospheric wave events and major sudden stratospheric warming (SSW) events are well captured in high-resolution global forecasts out to 10 days. Tropospheric influences of SSW include statistically significant shifts in the storm tracks and associated surface temperature and precipitation pattern changes. Since these events can in turn influence the troposphere on time scales of 30-60 days the ability to predict these events and the subsequent long-term response on time scales beyond 10 days is of interest. Here we examine the prediction of stratospheric wave events and their evolution using the NASA GMAO (Global Modeling and Assimilation Office) Sub-Seasonal to Seasonal (S2S) system. This is a recently released subseasonal to seasonal forecast system, GEOS-S2S version 2.1. Compared to GMAO's previous system, the new version runs at higher atmospheric resolution (approximately 1/2 degree globally), contains a substantially improved model of the cryosphere, includes additional interactive aerosol model components, and the ocean data assimilation system has been replaced with a Local Ensemble Transform Kalman Filter. Results are based on a comprehensive series of hindcasts starting from the year 2000. They show that while the S2S system is not as accurate at 10 days in forecasting major SSW events as the NASA GMAO Forward Processing system, it can usefully predict stratospheric anomalies out to 20 days and the subsequent stratospheric/tropospheric evolution beyond 30 days.