Unless the private investigator is an actual law enforcement officer then no private investigators cannot make arrests.
The only thing a private investigator can do is follow someone around and check out what they're doing and where they are going and then report that information to the person who hired the private investigators.
Private Investigators have to be very careful in what they do and how they follow someone because it can be considered stalking.
The private investigator cannot go onto the persons property but must remain on public property when doing the private investigations.