Modals express degrees of certainty.

Speculating about present are followed by a base form verb.
●You could be right.
●They should be very happy.

Speculating about the past are followed by the past participle.
●She could have won the lottery.

 Near centainty.
● He had to have robbed a bank.

Less Certain.
Modals + Have+ past participle
● She might have inherited some money from her family.
●She may have gotten a big raise at work.
●They must have moved to an exotic island