The Holy Spirit is God
The Holy Spirit is one of the three persons of the godhead. For God is triune; He is not a solitary person, but exists in the Father, the Son and the Holy Spirit. One of the most common pictures the Bible gives us to understand God in this way, is the picture of speaking. God the Father speaks the Word of God (the Son) by the breath of God (the Spirit).
That the Holy Spirit is fully God, becomes clear from various Bible texts that describe His character: The Holy Spirit is eternal (Hebrews 9:14), He is omnipresent (Psalm 139:7-10), He is omniscient (1 Corinthians 2:10-11), He is almighty (Luke 1:35-37), and He is holy (Romans 1:4).
The ancient Christian creeds
The ancient Christian creeds are the statements of belief which all Christian churches agree on. They describe the basic truths about God on which everything else in the Christian faith depends. The Athanasian Creed says about the Holy Spirit:
“Such as the Father is; such is the Son; and such is the Holy Ghost.
The Father uncreated; the Son uncreated; and the Holy Ghost uncreated.
The Father unlimited; the Son unlimited; and the Holy Ghost unlimited.
The Father eternal; the Son eternal; and the Holy Ghost eternal.
And yet they are not three eternals; but one eternal.
As also there are not three uncreated; nor three infinites, but one uncreated; and one infinite
[…] The Holy Ghost is of the Father and of the Son; neither made, nor created, nor begotten; but proceeding.”
For all eternity, the Holy Spirit proceeds from the Father and the Son, but this does not mean He is created by Them, nor does it make Him any less God than Them, nor any less a person than Them. It is just a way of describing the relationship they have always had. All members of the Trinity are ‘self-existent’, but also depend on each other to be the person they are: for example, the Father couldn’t be ‘father’ without the Son being ‘son’.
Speaker, Word and Breath
This is hard to understand, but think of the biblical picture of speaking again. You can imagine the Father, Son, and Spirit as “Speaker, Word, and Breath.” The breath would not be breath without the speaker and his word. The word would not be a word without the speaker and the breath which carries him. And the speaker would not be a speaker unless he was speaking the word on his breath.
This is a lovely picture of God who has for all eternity existed as someone telling a story or singing a song. The Bible describes God doing things by speaking. God speaks to create the world (Genesis 1:1-3, 6, 9, etc.), to keep the world going (Hebrews 1:3), and to save the world from our sins (Isaiah 55:11; 1 Peter 2:9).
The Holy Spirit has not been created
The Biblical evidence, thought through and summarized by the early church, clearly states that the Holy Spirit is God and thus has existed from the beginning. He has not been created, but was there from eternity.