We propose a new real-time temporal filtering and antialiasing (AA) method for rasterization graphics pipelines. Our method is based on Pixel History Linear Models (PHLM), a new concept for modeling the history of pixel shading values over time using linear models. Based on PHLM, our method can predict per-pixel variations of the shading function between consecutive frames. This combines temporal reprojection with per-pixel shading predictions in order to provide temporally coherent shading, even in the presence of very noisy input images. Our method can address both spatial and temporal aliasing problems under a unique filtering framework that minimizes filtering error through a recursive least squares algorithm. We demonstrate our method working with a commercial deferred shading engine for rasterization and with our own OpenGL deferred shading renderer. We have implemented our method in GPU and it has shown significant reduction of temporal flicker in very challenging scenarios including foliage rendering, complex non-linear camera motions, dynamic lighting, reflections, shadows and fine geometric details. Our approach, based on PHLM, avoids the creation of visible ghosting artifacts and it reduces the filtering overblur characteristic of temporal deflickering methods. At the same time, the results are comparable to state-of-the-art realtime filters in terms of temporal coherence.