Buddhists advise against "me and mine" does that include times?

Buddhists advise against "me and mine" does that include times? Do Buddhists really talk about "my" future past and present? If so, what are the nature of those times? Specifically: will "my" present always be "my" past? ---------- I'm just asking because I'm trying to work out if there's any reason to believe that, if this will be "my" past, will "I" then exist in the future. ---------- It's often said that impermanence is the Buddha self. Could that be one answer: and why believe it?