Correct spelling for the English word "Prestigiation" is [pɹˌɛstɪd͡ʒɪˈe͡ɪʃən], [pɹˌɛstɪdʒɪˈeɪʃən], [p_ɹ_ˌɛ_s_t_ɪ_dʒ_ɪ__ˈeɪ_ʃ_ə_n] (IPA phonetic alphabet).
The word "prestigiation" does not have any recognized etymology, as it is not a commonly used or widely recognized term in the English language. It is possible that "prestigiation" is a misspelling or a variation of the word "prestidigitation". Prestidigitation, on the other hand, comes from the French word "prestige", meaning "illusion", and the Latin word "digitus", meaning "finger". Therefore, prestidigitation literally means "quick-fingered" or "nimble-fingered", reflecting the art of performing magic tricks or sleight of hand. However, it is important to note that "prestigiation" is not a standard or recognized word, and its specific etymology is unclear.