Picture a timeline with actions on it. The only point in motion is the present. Only present actions are alive: past ones are dead and future ones, unborn.
Therefore, it makes sense to use the present perfect in the continuous to describe an action having started before the time of speaking and still going on at the time of speaking: present perfect continuous. With the continuous, you witness an action unfolding itself.
I have been saving money lately.
But then, if the action verb is in the negative, it can have two different meanings:
either the absence of any action,
or the implied presence of the contrary action.
In the first case, it would not make much sense to express a non-action in the continuous, paradoxically giving life to a non-entity.
I have not saved any money lately. * I have not been saving any money lately. *
Whereas, in the second case, it does make sense, because a real action – the contrary action – is meant.
I have not been saving money lately. (= I have been blowing money lately. / I have been spending wildly.)