Which time war? there were a few time wars. If you are talking about the Last Great Time War that is time locked, it's nearly impossible to tell. If certain accounts are to be believed, the "first shot" of the Time War was in "Genesis of the Daleks", but the time period it took place in is unknown. Considering it was a Time War, it could have been fought over multiple years and time periods.
According to "Engines of War" (novel), it lasted for several centuries from the point of view of the participants but, because time travel was used, assigning a length to the war is virtually meaningless.
In "The Night of the Doctor", it's made clear that the war had already lasted a long (but unspecified) time when the Eighth Doctor regenerated into the "War Doctor". Additionally, the "War Doctor" was shown as looking young in that story but had become old-looking between then & the events of "The Day of the Doctor", implying that centuries of his timeline had elapsed between the two stories.