  We fully classify automatic sequences $a$ over a finite alphabet $\Omega$
with the property that each word over $\Omega$ appears is $a$ along an
arithmetic progression. Using the terminology introduced by Avgustinovich,
Fon-Der-Flaass and Frid, these are the automatic sequences with the maximal
possible arithmetical subword complexity. More generally, we obtain an
asymptotic formula for arithmetical (and even polynomial) subword complexity of
a given automatic sequence $a$.
