Summary: In robotic radiosurgery, a photon beam source, moved by a robot arm, is used to ablate tumors. The accuracy of the treatment can be improved by predicting respiratory motion to compensate for system delay. We consider a wavelet-based multiscale autoregressive prediction method. The algorithm is extended by introducing a new exponential averaging parameter and the use of the Moore-Penrose pseudo inverse to cope with long-term signal dependencies and system matrix irregularity, respectively. In test cases, this new algorithm outperforms normalized LMS predictors by as much as 50\%. With real patient data, we achieve an improvement of around 5 to 10\%.