The title says "A Poem by David" (16:1), and the psalm says I all the way through. Was David speaking of himself?

The psalm speaks as I from its first line to its last (16:1, 16:11), and says nothing more of who the I is than its title. The New Testament answers the question twice, with an argument. Peter (Acts 2:14), speaking of "Jesus of Nazareth" (Acts 2:22), "whom God raised up" (Acts 2:24), says, "For David says concerning him" (Acts 2:25), and gives the words of 16:8-11 (Acts 2:25-28). Then he reasons from David's grave: "Brothers, I may tell you freely of the patriarch David, that he both died and was buried, and his tomb is with us to this day" (Acts 2:29). "Therefore, being a prophet" (Acts 2:30), "he foreseeing this, spoke about the resurrection of the Christ, that his soul wasn’t left in Hades, and his flesh didn’t see decay" (Acts 2:31). "This Jesus God raised up, to which we all are witnesses" (Acts 2:32). Paul, in the synagogue at Antioch (Acts 13:14-16), says, "Therefore he says also in another psalm" (Acts 13:35), gives the words of 16:10, and argues the same way: "For David, after he had in his own generation served the counsel of God, fell asleep, was laid with his fathers, and saw decay" (Acts 13:36). "But he whom God raised up saw no decay" (Acts 13:37). Both set David, who died, beside Jesus, whom God raised. These notes give their argument in their own words, and add nothing to it.