Question: can the byakugan predict movements?
Answer: No, the Byakugan can't predict movements. Only the Sharingan can do that. Neji's excellence at Taijutsu and swatting Kidomaru's attacks are simply due to him being ridiculous and having a huge field of vision. The only thing it should be able to “predict” is the use of jutsu because it see the flow of chakra.