Arecidae is a botanical name at the rank of subclass.
Circumscription of the subclass will vary with the taxonomic system being used (there are many such systems); the only requirement being that it includes the family Arecaceae.
The Takhtajan system[1] used this name for a subclass in the class Liliopsida (=monocotyledons).
The Cronquist system (1981) used this name for a subclass in the class Liliopsida (=monocotyledons), with the circumscription: The APG II system does not use formal botanical names above the rank of order; it assigns the plants included in this subclass by Cronquist in various taxa throughout the clade monocots.
In other words, by today's standards Cronquist's subclass was not a "good" group.