The English modal verbs are often challenging for learners
of English. This happens for many reasons, including both
grammar and meaning.

In this Hint, we'll take a look at could have.

We know from earlier Hints that could has many uses. Several
of them are used for present or future time, but could is also
used to show ability in the past.

Could also has another past form--could have. This form is
followed by the past participle of the main verb:

could have been / could have gone / could have finished /
could have seen / could have done / could have taken / etc.

When could is used in this way, it refers to possibility in the
past. It does not refer to ability or permission in the past.

Examples:

I don't know why Bill left early. He could have had
some kind of emergency, I suppose.

(I don't know why Bill left early. Maybe he had
some kind of emergency.)

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I'm not sure where I met her. It could have been at a party
or it could have been been at a business meeting.

(I don't remember where I met her. Maybe I met her
at a party or maybe I met her at a business meeting.)

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I know he was at home, but he didn't answer the phone.
He could have been asleep or taking a shower, I suppose.

(I know he was at home, but he didn't answer the phone.
Maybe he was asleep or taking a shower.)

The negative form of could have is could not have (which is
often contracted to couldn't have). Couldn't have is also
followed by the past participle of the main verb. It's used to
show someone's feeling that something in the past is impossible.

Examples:

You couldn't have seen Jerry yesterday. He's been out of
town since last Tuesday!

(It's impossible for you to have seen Jerry yesterday because
he wasn't here. He's been out of town since last Tuesday!)

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Suzie's daughter couldn't have drawn this. She's only
two years old!

(It's impossible for Suzie's daughter to have drawn this
because it's too sophisticated. Suzie's daughter is only
two years old!)

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Bill couldn't have written this letter. There are no spelling
mistakes, and Bill is a terrible speller!

(It's impossible for Bill to have written this letter because
there are no spelling mistakes, and Bill is a terrible speller)

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Special Notes: