These particular shouts of approbation, encouragement or exultation date back to the late 17th century. According to the OED, hurrah is the literary and dignified spelling, while hooray is the popular form. Hoorah would be the preferred, popular spelling in America. All these variations derive from the earlier shout of huzza which would have been widely used in the 16th century by equestrians as a cry of exultation or pursuit. One is tempted to think that perhaps the word hussar derives from the same source, but not so.