Hello, Of course someone could think that we could produce output before the input occurs but the solution is much more simpler. In the referred examined area, the group delay and the ampliture do not exhibit constant values. E.g. A signal which would pass through this filter in the specific area-region it would be distorted due to the aforementioned while the apparent delay would be presented as negative which is not the real thing.

Please also see the following:

Article Group delay explanations and applications

As I recall, resonance modes with negative group speed (akin to group delay) are possible in floating solid plates. Their interpretation comes from the wider analysis of the resonances in the structure. In the plate, a mode with negative group speed always has a companion resonance with a positive group speed. You cannot physically excite one of the pair without exciting the other. The phenomenon is therefore not an isolated resonance with negative group speed but of resonance +/- pairs that together constitute standing waves. You might have a situation similar to that.

For a narrow-band signal you should probably be looking at phase shift instead of group delay. Anyway ...

For a broad-band wave-packet (i.e. pulse-like) a +ve group delay means that the pulse is shifted back in time as it passes through a system or filter; whereas a -ve group delay means it is shifted forward in time.

The latter case doesn't necessarily violate causality, it just means that the filter predicts where the pulse will be in the future, based on where it is now.