Per the dictionary there is no shortcut for Hooray, but yay does does fit the pronunciation of Yippee-ki-yay! Yeah, or yea is short for yes. July 18, 'Yeah' is an affirmative adverb, much like 'certainly' 'indeed' and 'yes' - which can function as an adverb as well as an interjection. Also, to save two letters (keystrokes) in texting is lazy and dumbing down the language, but that horse has left the barn, eh? When I see 'Ya' or 'yah' my brain hears Arnold Schwarzenegger, so I write 'yeah'. For clarity I type the word 'yeay' (not yay or yea) because you can hear the 'y' at the end of the word. Hearing words and typing/reading words have some differences. It is as if the movie industry is trying to push it artificially, or at least that's my observation as a non-native English speaker. Is it just me, or in recent years, do US movies and TV shows try to push 'ya'? Many shows that have lots of seasons and are on air for years have started using 'ya' instead of 'yes' very noticeably in the last year or so. As to the spellings of 'yah' and 'yay', these are just uneducated spellings, not important.
citizens west of New York and east of the western mountain states have Teutonic or Scandinavian ancestors, so 'Ja' is their 'Yes'. 'Jah' typically spelled 'Ja' is German for 'Yes', Swedish for 'yes', Danish for 'yes', and Norwegian for 'yes'.