Sentence Grammar

Is this Analysis OK for this sentence?

A fine Arab horse race is on sale this week at the Royal farm.

A: Determiner (Article)
Fine: Adjective Arab: Adjective
fine Arab (Adjective Phrase)

horse race: Noun.

“A fine Arab horse race is on sale” is not correct (or at best needs a pretty unusual context).

Did you mean “A fine Arab horse is on sale”?

[edited] … oh, I guess you may mean “a fine Arab racehorse