have + been + verb-ing

The perfectThe aspect expressing completion. E.g.: He’s finished university. continuousThe aspect expressing duration, formed with be + verb-ing. E.g.: What are you doing? is not considered as an aspectA verbal category relating an action to the passage of time. It can express duration or completion. in itself; rather it is the combination of the perfect and continuous aspects.

It is expressed with the auxiliariesA helping verb used with main verbs to express mood, voice and tense. E.g.: I can't stand when I am disturbed. ("can", "am") have and been (the third form of be), and the (present participle) -ing form of the verb. Depending on the timeA concept which is related to our perception of reality; that part of existence which is measured in seconds, minutes, hours, days, weeks, etc. of the actionA general term expressing that somebody or something does something, we use the past (had), present (have, has) or modal + infinitive (e.g. would have) form of have.

The perfect continuous expresses that the action had, has or will have been in progressAn action is in progress when it is happening. E.g.: When I arrived he was surfing. ("he was surfing") for some time at a particular point of timeA particular moment in time. E.g.: She came home at six. ("six") I was born in 1980. ("1980") . This point of time may be defined by a time expressionA word or group of words used in a particular situation. E.g.: Good morning, at six, on the sofa (at 5 o'clock) or a clauseA group of related words containing a subject and a verb. (when she gets home).

Examples of the perfect continuous:

I've been waiting for this moment all my life. (from when I was born until now)
At 5 o'clock he had been writing his homework for an hour. (from 4 to 5 o'clock) 
When she gets home, Kevin will have been sleeping for hours. (from some time before she gets home until she gets home)
He's been ironing his shirts. (from some time in the past until now) 
I wouldn't have been sitting there, if I hadn't had to. (from some time in the past until a later time in the past) 

Diagrams

The perfect aspect
Aspects State verbs and action verbs / Verbs not used in the continuous form