All the books of the bible outside of
Paul's 13 epistles are considered books of "Prophecy"
by God.

They all teach the Nation of Israel to look forward to
their long promised Messiah and His kingdom of Heaven
on earth for them.

In 2 Peter 2:21, Peter is explaining to Israel the
delay in their kingdom coming (because of Paul's
message...the present Dispensation of Grace to us
Gentiles)...and Peter says that all those Old Testament
books to Israel are called "prophecy".

2 Peter 2:21...For the prophecy came not in old time
by the will of man: but holy men of God spake as they
were moved by the Holy Ghost.

One of these "holy men" that were moved by the Holy
Ghost and wrote these prophecies is David, who wrote
most of the Psalms.

Earlier in the book of Acts, Peter explains to the mne
of Israel that those things that were written in the
Old Testament spoke of a future time to come (the
kingdom)..which is the definition of prophecy.

Acts 3:18-21...But those things, which God before had
shewed by the mouth of all his prophets, that Christ
should suffer, he hath so fulfilled. 19 Repent ye
therefore, and be converted, that your sins may be
blotted out, when the times of refreshing shall come
from the presence of the Lord; 20 And he shall send
Jesus Christ, which before was preached unto you: 21
Whom the heaven must receive until the times of
restitution of all things, which God hath spoken by the
mouth of all his holy prophets since the world began.

In Acts 4, Peter says that what David wrote in Psalms
is a passage that was being fulfilled as Israel was
about to enter into the prophesied Tribulation
period/Day of the Lord:

Acts 4:24-28...And when they heard that, they lifted up
their voice to God with one accord, and said, Lord,
thou art God, which hast made heaven, and earth, and
the sea, and all that in them is: 25 Who by the mouth
of thy servant David hast said, Why did the heathen
rage, and the people imagine vain things? 26 The kings
of the earth stood up, and the rulers were gathered
together against the Lord, and against his Christ. 27
For of a truth against thy holy child Jesus, whom thou
hast anointed, both Herod, and Pontius Pilate, with the
Gentiles, and the people of Israel, were gathered
together, 28 For to do whatsoever thy hand and thy
counsel determined before to be done.

And one more passage...the Lord Jesus Himself, during
His earthly ministry to Israel says that what David
wrote in Psalms was a prophectic look into the future
Tribulation/kingdom:

Mark 12:36...For David himself said by the Holy Ghost,
The LORD said to my Lord, Sit thou on my right hand,
till I make thine enemies thy footstool.

This is a passage explaining the wrath of God being
poured out during the Tribulation period (future from
us) and the Lord Jesus Christ setting up His earthly
kingdom in Israel in the future.

So yes, the book of Psalms (and all the "poetic" books
of Job thru Song of Solomon) are not only historical
books for Israel, but they are also prophectic books
looking towards the future!

James also uses the book of Job (and calls him a
prophet) for that very purpose! Job is the oldest book
of the bible, but James tells Israel in Job
5:10-11...Take, my brethren, the prophets, who have
spoken in the name of the Lord, for an example of
suffering affliction, and of patience. 11 Behold, we
count them happy which endure. Ye have heard of the
patience of Job, and have seen the end of the Lord;
that the Lord is very pitiful, and of tender mercy.

As Israel in the future reads the book of Job, they can
endure the persecution of the AntiChrist by seeing how
God was faithful to deliver Job from Satan's attack as
well!