Yours, Etc.: Origins and Uses of 8 Sign-Offs
1680s, type of firework, from sky (n.) + rocket (n.2). The verb, in the figurative sense of "to rise abruptly and rapidly" (often with suggestion of 'and then explode and vanish'") is attested from 1895.
To increase rapidly: Profits are expected to skyrocket after the announcement (1895+)