The postulation that it was erected well before the Romans invaded the region is based on ceramic finds at some of the archaeological sites on or near the wall that pre-date the Romans. However, the pottery sherds found are too few to be clearly indicative of the period or periods the walls were in use. Fieldwork has yielded ceramics from almost all time periods. However, the ceramic evidence predominantly date to the Iron Age.Background here. The earlier article suggested the wall may have been built "sometime between the Nabataean period (312 B.C.–A.D. 106) and the Umayyad period (A.D. 661–750)." So the Nabataeans (Nabateans) are still in the running as possible builders, but it may have been built well before their time. It sounds as though we're still in the realm of speculation.
Most likely, says [David[ Kennedy, [head of the expedition and a researcher from the University of Western Australia] the wall was built in stretches, perhaps over a long period of time. “More fieldwork should be directed to some of the places where there is a settlement site associated with the wall. Dating the settlement and determining its exact relationship to the wall may provide a closer and more reliable guide to date. My best guess is that it is Iron Age or Nabataean.”
“We have known about this enigmatic wall feature for decades now, but the interesting contribution of the new research is the suggestion that it is pre-Roman," Erez Ben-Yosef from Tel Aviv University, who worked in southern Jordan and currently heads the Timna Valley Project, told Haaretz. "It might be related to the border administration of the Nabataeans or the Edomites, but as was stated by Kennedy and his colleagues, more definite answers should await field research.”
The wall and towers are just one of the many enigmatic features being found in the deserts of Jordan referred by the Bedouins as "The Works of the Old Men.” Giant geoglyphs and earthworks in the shape of rings, kites, and wheels, practically invisible on the ground but clearly evident from the air, have given rise to theories – some rather wacky - but very few answers.
Dr. Ben-Yosef and the Timna Valley excavation were also in the news earlier this week.