Pilot reported reported a NMAC while practicing maneuvers near a non-towered airport.

Narrative

After takeoff; I was heading to Location X about 5 NM west from ZZZ. Another aircraft (female voice) made a call announcing they were doing chandelles at or around 3000 MSL over XXX.XX. I was at or around 4500 MSL climbing to 5500 MSL. I made a call over XXX.XX that I was heading towards ZZZ Airport to do chandelles at 5500 MSL. when I arrived I heard the female voice call they were now over ZZZ doing chandelles. I do not recall the altitude but it was below me. I made a call on the radio again to announce I was directly over ZZZ airport; 5500 MSL doing chandelles. The aircraft then went back to Location X to continue their manoeuvers without incident. I made frequent calls on the radio announcing I was over ZZZ airport doing chandelles and/or lazy eights at or around 5500 MSL. I think around XA00. Another aircraft (male voice) announced they were over ZZZ airport; same altitude (5500 MSL) doing manoeuvres. I believe chandelles. I immediately made a call on the radio to announce I was over ZZZ airport doing chandelles. I had no response. I notice the aircraft was still heading towards me +100 feet according to my G1000 traffic. I immediately began a descending turn away from the aircraft to get as far under it in the shortest time. I then announced on the radio (XXX.XX) I was leaving the ZZZ airport area. I never had eyes on the aircraft; only G1000 traffic system. I felt that aircraft was too close for comfort and either choose to ignore my radio calls and did not hear them. This is an area with usually low traffic (3000 MSL) so I do make as many calls as possible to avoid any incidents such as today's. I typically make one after I complete my 180 turn after a chandelle or lazy eight.