Modals of speculations

What are modals of speculation?
Modal auxiliary verbs express degrees of certainty.  In other words, they describe a fact or situation that is definite, probable, possible, or impossible.  However,despite the degree of certainty (or uncertainty), the speaker may be wrong.  Here we'll focus on speculating about past events.  For example:
    A: Kelly must have gone somewhere tropical forvacation, because she's sunburned.
    B: Actually, I she got some free tickets for a tanning salon.  She didn't go anywhere last week.
What is the sentence structure?
The sentence structure is asfollows:
    subject  |  modal verb  |  (negation)  |  have  |  past participle  |  object/complement
    Mary  |  must  |  (not)  |  have  |  done  |  well on the test.
    Jennifer  |  could  | (not)  |  have  |  made  |  as much money as she claims.
How are modals of speculation used?
Commonly used modals for past events include the following:
Must have expresses a definite situation,and must not have /could not have an impossible one.  When we use may have /may not have, we aren't as certain.  And when expressing weak probability, use might have /might not have /could have.
+ Shemust have gone somewhere tropical for vacation, because she's sunburned.
-  She must not (mustn't) have enjoyed her weekend skiing, because she broke her leg!
+ Alex may have spent some time inParis because he often talks about the city.
-  Alex may not have enjoyed Paris, because he rarely says anything positive about the city.
+ The economy might have gotten worse without the tax cuts.-  The tech bubble might not have happened if people had invested more carefully.
+ Kerry could have won the 2004 election if he had responded to the attacks on his character.
-  Gore could not(couldn't) have won the 2000 Presidential election.
Is there additional information on modals of speculation?
Yes, there is.  When speculating about past events, the sentence must use have + past...