We used telemetry data from the Gemini North ALTAIR adaptive optics system to investigate how well the commands for wavefront correction (both tip/tilt and high-order turbulence) can be forecasted to reduce lag error (due to wavefront sensor averaging and computational delays) and improve delivered image quality. We showed that a high level of reduction (∼5 for tip-tilt and ∼2 for high-order modes) in the RMS wavefront error was achieved using a “forecasting filter” based on a linear autoregressive model with only a few coefficients (∼30 for tip-tilt and ∼5 for high-order modes) to complement the existing integral servo-controller. Updating this filter to adapt to evolving observing conditions is computationally inexpensive and requires <10  s of telemetry data. We also used several machine learning models (long-short term memory and dilated convolutional models) to evaluate whether further improvements could be achieved with a more sophisticated nonlinear model. Our attempts showed no perceptible improvements over linear autoregressive predictions, even for large lags in which residuals from the linear models are high, suggesting that nonlinear wavefront distortions for ALTAIR at the Gemini North telescope may not be forecasted with the current setup.