Do people who prognosticate have some sort of special power?
Anyone can be a prognosticator. All it takes to prognosticate is a look around at current events and an opinion about what may unfold in the future. Prognostications are predictions based on impressions of what's happening today.
In George Eliot's Adam Bede, aristocratic Mrs. Irwine says, "I suppose Carroll has told you that Donnithorne was found dead in his bed this morning. You will believe my prognostications another time, though I daresay I shan't live to prognosticate anything but my own death."
Mary Shelley wrote in Frankenstein, "On the third day my mother sickened; her fever was accompanied by the most alarming symptoms, and the looks of her medical attendants prognosticated the worst event."
Prognostications are not solely related to death or dying, as evidenced in Thomas Hardy's The Mayor of Casterbridge: "At twelve o'clock the rain began to fall, small and steady, commencing and increasing so insensibly that it was difficult to state exactly when dry weather ended or wet established itself. In an hour the slight moisture resolved itself into a monotonous smiting of earth by heaven, in torrents to which no end could be prognosticated."