MD-80 Series (DC-9-80) Undifferentiated or Other Model
Flight Crew Air Transport Pilot (ATP)
ATC Issue All Types; Conflict NMAC; Deviation - Altitude Excursion From Assigned Altitude; Deviation / Discrepancy - Procedural Clearance
Air Traffic Control Issued Advisory / Alert; Flight Crew Took Evasive Action
Procedure; Airspace Structure
On approach to Airport ZZZ the approach controller called out a traffic target at our 10 O' Clock position about 500 feet below us.  We did not see the traffic immediately; but had them on TCAS.  The controller issued a left turn vector toward the traffic and indicated that the aircraft had turned away from us.  I spotted the traffic visually and it appeared to be a single engine aircraft doing turns around a point in the VFR/General Aviation practice area clear of the Class D for ZZZ. As it continued its turn and began to fly towards us again; we got a 'monitor vertical speed' aural warning.  The traffic then appeared to start climbing and we received an 'adjust vertical speed' command.  The FO disconnected the autopilot and promptly responded to the CLIMB command.  We were clear of conflict within seconds and reported the RA to ATC as well as asked for a NMAC report to be filed.  After landing I was given a phone number to the [approach control] supervisor.  I explained to him what happened; which also mirrored what his controller had reported to him.  He said he would file a NMAC report.
MD80 Captain at 2;800 feet approaching destination is advised by ATC of traffic at 10 O'clock and 500 feet below; then is issued a vector toward the traffic. The traffic starts to climb resulting in a TCAS TA then an RA. The Captain asks ATC to file an NMAC report.