Senecio arborescens should be a species of the genus Senecio

Senecio

Senecio is a genus of the daisy family that includes ragworts and groundsels. The flower heads are normally rayed, completely yellow, and the heads are borne in branched clusters...

 in the Asteraceae

Asteraceae

The Asteraceae or Compositae , is an exceedingly large and widespread family of vascular plants. The group has more than 22,750 currently accepted species, spread across 1620 genera and 12 subfamilies...

 family, but the available information about it mostly conflicting and old.

According to the World Conservation Union

World Conservation Union

The International Union for Conservation of Nature and Natural Resources is an international organization dedicated to finding "pragmatic solutions to our most pressing environment and development challenges." The organization publishes the IUCN Red List, compiling information from a network of...

, S. arborescens is a native to and widely occurring in the area ranging from Mexico

Mexico

The United Mexican States , commonly known as Mexico , is a federal constitutional republic in North America. It is bordered on the north by the United States; on the south and west by the Pacific Ocean; on the southeast by Guatemala, Belize, and the Caribbean Sea; and on the east by the Gulf of...

 to possibly Colombia

Colombia

Colombia, officially the Republic of Colombia , is a unitary constitutional republic comprising thirty-two departments. The country is located in northwestern South America, bordered to the east by Venezuela and Brazil; to the south by Ecuador and Peru; to the north by the Caribbean Sea; to the...

. John Claudius Loudon

John Claudius Loudon

John Claudius Loudon was a Scottish botanist, garden and cemetery designer, author and garden magazine editor.-Background:...

 says that S. arborescens is a synonym for Baccharis halimifolia

Baccharis halimifolia

Baccharis halimifolia is a fall-flowering deciduous or evergreen shrub commonly found in wetlands on the Atlantic and Gulf coastal plains of the eastern United States from Texas and Florida northward to Massachusetts, inland to the District of Columbia and Pennsylvania...

and native of the United States from "Maryland

Maryland

Maryland is a U.S. state located in the Mid Atlantic region of the United States, bordering Virginia, West Virginia, and the District of Columbia to its south and west; Pennsylvania to its north; and Delaware to its east...

 to Florida

Florida

Florida is a state in the southeastern United States, located on the nation's Atlantic and Gulf coasts. It is bordered to the west by the Gulf of Mexico, to the north by Alabama and Georgia and to the east by the Atlantic Ocean. With a population of 18,801,310 as measured by the 2010 census, it...

, on the sea coast" in his 1842 catalog of trees and shrubs and Raymond Taylor agrees with this in his 1952 catalog of Plants of Colonial Days, which also claims that the plant is native to New Jersey

New Jersey

New Jersey is a state in the Northeastern and Middle Atlantic regions of the United States. , its population was 8,791,894. It is bordered on the north and east by the state of New York, on the southeast and south by the Atlantic Ocean, on the west by Pennsylvania and on the southwest by Delaware...

 and was introduced to Collinson

Peter Collinson FRS

Peter Collinson was a Fellow of the Royal Society, an avid gardener, and the middleman for an international exchange of scientific ideas in mid-18th century London...

 in England from John Bartram

John Bartram

*Hoffmann, Nancy E. and John C. Van Horne, eds., America’s Curious Botanist: A Tercentennial Reappraisal of John Bartram 1699-1777. Memoirs of the American Philosophical Society, vol. 243. ....

 in Cape May

Cape May

Cape May is a peninsula and island ; the southern tip of the island is the southernmost point of the state of New Jersey, United States. It runs southwards from the New Jersey mainland, separating Delaware Bay from the Atlantic Ocean...

 in 1683.
And a group of botanists under the discipline of Hieronymum Lentzium seem to have attempted to record the species as a Cacalia

Cacalia

Adenostyles, is a large genus of to a flowering plants in the sunflower family Asteraceae, and of the constantly changing tribe Senecioneae...

when they drew a nice image of a completely different plant for their 1737-1745 catalog.