word usage - So, "might have been sleeping" (Modal perfect continuous) corresponds to past continuous, present perfect continuous or past perfect continuous?

"Modal + have + PP" refers to the past

But it is quite ambiguous!!

What does "the past" mean?

Simple Past, Present perfect, Past perfect all refers to the past.

So the question is:

Does Modal + have + PP" refer to Simple Past, Present perfect, or Past perfect?

Similarly,

Does Modal + have + been + Verb-ing" refer to Past Continuous, Present perfect continuous, or Past perfect continuous?

Ok, let say, now is 3 pm. At 2 pm (1 hour earlier) you walked by a baby room & you didn't hear any noise.

Now, you say this to your friend:

The baby might have been sleeping.

Does that sentence mean:

"It is possible that the baby was sleeping"

OR

"It is possible that the baby has been sleeping (ie unfinished action & the baby is still sleeping now)"

OR

"It is possible that the baby had been sleeping (ie the baby had been sleeping possibly for 30 minutes, but now she is awake)"

But, if you says "The baby might have been sleeping by the time I was home yesterday", we can be sure that means "It is possible that the baby was sleeping by the time I was home yesterday"

if you says "The baby might have been sleeping for 1 hour" (Now is 3pm, & you walked by the baby room at 2pm), we can be sure that means "It is possible that the baby has been sleeping for 1 hour (he is still sleeping now, unfinished action)"

if you says "The baby might have been sleeping for 30 minutes" (Now is 3pm, & you walked by the baby room at 2pm), we can be sure that means "It is possible that the baby had been sleeping for 30 minutes (an action happened in the past and had progressed continuously to another point in the past)"

So, "might have been sleeping" (Modal perfect continuous) corresponds to past continuous, present perfect continuous or past perfect continuous?

Note: could you include a referenced source in your answers because I need some evidence while teaching students?

Answer

Finally, I can find the answer in here