It is absolutely appropriate and biblical to pray to the Holy Spirit and to Jesus. Along with God the Father, Jesus and the Holy Spirit are fully God and are equal in every way to the Father and to each other. It's one of the foundational truths of Christianity that God is one God in three Persons--Father, Son, and Holy Spirit.

Having said that, is there a "pattern" for prayer that is exemplified in Scripture? There seems to be, especially in the prayers of Jesus. Jesus is God incarnate--that is, God in the flesh (John 1:14)--who came to earth as the visible image of the invisible God (Colossians 1:15). Jesus came, not only to live a perfect life so He could become the perfect substitutionary sacrifice for sin on our behalf, but also to show us how to live.

So, if we are to imitate Jesus in our prayers, it is appropriate to pray to the Father in the name of Jesus, and in the power of the Holy Spirit. As a theologian friend once told me, this is praying "with the grain" of Scripture. But again, there's nothing wrong with praying to any Person in the Trinity.