Air carrier Captain reported receiving traffic alerts from his TCAS even though ATC reported no aircraft in his vicinity.

Narrative

Traffic Collision Avoidance System Traffic Advisory on Approach. Was Pilot Flying on Flight ZZZ-RSW. Flew the SHFTY 5 RNAV Arrival for the ILS Runway 06. Handed off to RSW Approach. Was instructed to expect the visual Runway 06 with vector over Estero Bay. Given a northwest vector (right-base-to-final) before PONTY intersection. Cleared for the visual by approach inside of TROPC intersection (IAF; D12.6 IRSW) I selected 1500 ft. into the Altitude Window for DOLPN (FAF) and pulled Open Descent. I armed the approach mode. To the best of my memory; I know we were inland of the bay; approximately 2 miles before DOLPN when capturing the localizer. The aircraft was approximately between an altitude of 1700 ft. to 1500 ft. descending when I viewed an intermittent proximate intruder Traffic Collision Avoidance System display. It was visible; gone; visible at first and quite erratic. I was already in the 10 mile range. The First Officer and I immediately began a quick scan for traffic in the area. At about the time the aircraft captured 1500 ft.; we received an aural 'Traffic; Traffic' TA advisory. However; I saw no amber TA intruder symbol but a white proximate traffic symbol showing 1500 ft. below our altitude which was still at 1500 ft. We both continued our scans; and the target disappeared. The First Officer queried the Tower for any known traffic in the area; to which he responded no. We continued the approach; caught the glide slope and landed uneventfully. [The cause was the targets were] erratic; realistically made no sense with the altitudes; not visible to the crew; and unknown to ATC.