The Deity of the Holy Spirit Shown in the Old Testament

One does not need to search the New Testament to find passages proving the deity of the Holy Spirit. While it is true that the New Testament shows the Spirit to be divine, the Old Testament is not silent on this issue either.

Let's look at David's last words as recorded in second Samuel.

Now these are the last words of David. 

David the Son of Jesse declares, the man who was raised on high declares, the annointed of the God of Jacob, and the sweet psalmist of Israel,

"The Spirit of the LORD spoke by me, and His word was on my tongue. The God of Israel said, the Rock of Israel spoke to me..."

                     (2 Samuel 23:1-3 NASB)

In these three verses David states that the Spirit of YAHWEH spoke by him. What follows in this passage is a prophetic utterance spoken through David, by the Holy Spirit. 

Notice however it also states that the God of Israel said, the Rock of Israel spoke...

This is a hebraic way of stating a fact. The text is showing us that the Spirit of the LORD, the God of Israel, and the Rock of Israel are the same.

Who is the God (Elohim) of Israel? Who is Israel's Rock?  

"Thus says the LORD, the King of Israel and his Redeemer, the LORD of hosts: 

'I am the first and I am the last, and there is no God besides Me.

'Who is like Me? Let him proclaim and declare it; yes let him recount it to Me in order, from the time that I established the ancient nation. And let them declare to them the things that are coming and the events that are going to take place.

'Do not tremble and do not be afraid; have I not long since announced it to you and declared it? And you are My witnesses. Is there any God besides Me, or is there any other Rock? I know of none.'"

               (Isaiah 44:6-8 NASB)

We see in this passage that the God of Israel is the LORD YAHWEH. He is Israel's Rock, there is no other. So taking these passages together we can see that the Spirit of the LORD is divine. The Spirit is God, YAHWEH. The Holy Spirit cannot be another God, and Israel does not have two or more Gods. The text we have just read explicitly states that there is no other God, no other Rock. 

When David spoke prophetically by the Spirit, it was God speaking through him. Thus we can see that God has revealed Himself as the triune God in the Old Testament also.