As the others have said, the Bourne Shell doesn't have true arrays.
However, depending on what you need to do, delimited strings should suffice:
sentence="I don't need arrays because I have delimited strings"
for word in $sentence
do
printf '%s\n' "$word"
done
If the typical delimiters don't suffice, you can also play around with setting [IFS][1] to whatever delimiter you want before the loop.
And if you need to build the array programmatically, you can just build up a delimited string. [1]: https://en.wikipedia.org/wiki/Internal_field_separator
