What kind of verb form is used to indicate the perfect progressive tense?

It has auxiliary verbs before present participle (-ing form of a verb).

Examples with jumping as the present participle:

The past perfect progressive is formed with had + been + jumping. I/we/you/he/she/it had been jumping.

The present perfect progressive is formed with has/have + been + jumping. I/we/you/they have been jumping, he/she has been jumping.

The future perfect progressive is formed with will + have + been + jumping. I/we/you/he/she/they will have been jumping.