From Online Etymology:
1569, from Fr. inauguration "installation, consecration," from L. inaugurationem (nom. inauguratio) "consecration, installment under good omens," from inaugurare "take omens from the flight of birds, consecrate or install when such omens are favorable," from in- "on, in" + augurare "to act as an augur, predict" (see augur).
augur - c.1374 (implied in augury), from L. augur, a religious official in ancient Rome who foretold events by interpreting omens, perhaps originally meaning "an increase in crops enacted in ritual," in which case it probably is from Old L. *augos (gen. *augeris) "increase," and is related to augere "increase" (see augment). The more popular theory is that it is from L. avis "bird," since flights, singing, and feeding of birds or entrails from bird sacrifices were an important part of divination (cf. auspicious). The second element would be from garrire "to talk." The verb is 1549, from the noun.
Omens, predictions, consecration, increase, birds, flight, singing-talk-oratory, divination.
It really does feel like an inauguration day.