In one episode, Daisuke goes back in time. He witnesses the fight between a violinist and his grandfather (when he was as old as Daisuke). His grandfather faints, and Daisuke takes the brunt of the attack that would have killed the grandfather. Then, before the grandfather re-awakens, he returns to the present. Daisuke recounts the events to the grandfather (now an old man), and he says: "Oh, so it was you who saved me then!"
The other episode featured Daisuke travelling forward in time. He encounters a young boy, who calls his mom 'grandmother'. Daisuke is an only child, so that means this kid is his son. The kid has something that he needs, and he coax the kid to give it back to him, helped by his mom who recognizes him. Daisuke has to get back to the future and his time is running out. He mentions this to his mother, and she says: "This child is the proof that you are going to make it in time."
I'm amused that the plots of an anime series is consistent with the way time travel works in the Continuum game.