The Trinity is not explicitly stated in the Scripture. It is something the Church constructed as an intellectual effort, from the revealed truths. The revealed truths are mostly in the temporal domain. For example, the begetting of the Son is not described in the scripture as a primordeal event, Rather, it is postulated "I was there in the beginning" and then the Christmas incarnation, which is a temporal event, explains the relation between the Father and the Son. Similarly, the Holy Ghost is postulated as a primordeal person in the Genesis, and then a temporal event, the Pentacost, explains the relation between the Son (with the Father implied) and the Holy Ghost.
The event establishes the Holy Ghost as a distinct Person of the Trinity, but it can't establish the eternal relationship of the Holy Ghost to the other Persons of the Trinity, since it is a temporal event.
My two cents, anyway.
The Trinity is not explicitly stated in the Scripture. It is something the Church constructed as an intellectual effort, from the revealed truths.
The Church fathers were influenced in their trinitarianism by the neo-Platonists (including Plotinus, Proclus and the Pseudo-Dionysius). These guys characterized the fundamental triplicity at the root of things as follows:
mone (remaining, abiding); proodos (going forth); epistrophe (returning, turning back).
mone became "God, the Father" (Who abides in Himself); proodos became "Jesus, the Son of God" (Who goes forth into the world); and epistrophe became "The Holy Spirit" (Who mediates the return to the Father).
Of course, the neo-Platonists weren't called neo-Platonists for nothing; they owed most of the deepest aspects of their thinking to (their interpretations of) Plato's writings, and this includes their trinitarianism. But that's a matter for another post at another time.