The northern polar stratosphere plays an important role in modulating wintertime near-surface temperatures in midlatitudes. Forecasting northern polar stratospheric variability therefore has the potential to extend the skill of seasonal winter weather forecasts. This research explores the utility of state-of-the-art statistical learning models for medium-range (10-20 day lead time) forecasting of northern polar stratospheric variability. In addition to indices representing the El Niño Southern Oscillation, the Quasi-Biennial Oscillation, and the 11-year solar cycle, indices of the upward flux of wave activity from the troposphere into the stratosphere (WAF) are used as predictors for modelling and forecasting stratospheric temperature and geopotential height anomalies. The WAF is known to provide the primary source of intraseasonal variability in the wintertime stratospheric polar vortex. Multiple linear regression, random forest, artificial neural network, and support vector regression (SVR) models were trained over the 1980-2005 time period, and replicated real-time forecasts were generated for the 2005-2011 time period. The highest correlation skill for 10-day forecasts (ρ =0.41 for temperature, and ρ =0.49 for geopotential height) was found using the SVR model, which represents an improvement in skill over previous work that did not include WAF, or lagged predictors. Using a permutation-based method the importance of each predictor was ranked, and the WAF predictors were found to be most important for improving forecast skill in all models. In addition to improved forecast skill, it is argued that the methods presented here represent an advance due to their increased simplicity and relative ease of physical interpretation.