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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?

These are covered in the:

• 15 Wrong / Right Views


• 16 Doubts


• 
  108 thought-courses motivated by craving mentioned in this answer
  

15 Wrong / Right Views

Let go of the past

“How, bhikshus, does one pursue the past?

(1) One seeks delight there, thinking: ‘I had such form in the past.’

(2) One seeks delight there, thinking: ‘I had such feeling in the past.’

(3) One seeks delight there, thinking: ‘I had such perception in the past.’

(4) One seeks delight there, thinking: ‘I had such formations in the past.’

(5) One seeks delight there, thinking: ‘I had such consciousness in the past.’

This is how, bhikshus, one pursue the past.

And how, bhikshus, does one not pursue the past?

(1) One does not seek delight there, thinking, ‘I had such form in the past.’

(2) One does not seek delight there, thinking: ‘I had such feeling in the past.’

(3) One does not seek delight there, thinking: ‘I had such perception in the past.’

(4) One does not seek delight there, thinking: ‘I had such formations in the past.’

(5) One does not seek delight there, thinking: ‘I had such consciousness in the past.’

This is how, bhikshus, one does not pursue the past.

Let go of the future

And how, bhikshus, does one hold fond hope for the future?

(6) One seeks delight there thinking, ‘May I have such form in the future.’

(7) One seeks delight there, thinking: ‘May I have such feelings in the future.’

(8) One seeks delight there, thinking: ‘May I have such perception in the future.’

(9) One seeks delight there, thinking: ‘May I have such formations in the future’

(10) One seeks delight there, thinking: ‘May I have such consciousness in the future.’

This is how, bhikshus, one holds fond hope of the future.

And how, bhikshus, does one not hold fond hope for the future?

(6) One does not seek delight there, thinking, ‘May I have such form in the future.’

(7) One does not seek delight there, thinking: ‘May I have such feelings in the future.’

(8) One does not seek delight there, thinking: ‘May I have such perception in the future.’

(9) One does not seek delight there, thinking: ‘May I have such formations in the future’

(10) One does not seek delight there, thinking: ‘May I have such consciousness in the future.’

This is how, bhikshus, one does not hold fond hope of the future.

Let go of the present

And how, bhikshus, is one dragged along [distracted] by each present state as it arises?

(11) Here, bhikshus, an untaught ordinary person, who has no regard for the noble ones and is unskilled and undisciplined in their Dharma, who has no regard for true persons and is unskilled and undisciplined in their Dharma,

regards
- form as self, or
- self as possessed of form, or
- form as in self, or
- self as in form.

(12) He regards

• feeling as self, or


• self as possessed of feeling, or


• feeling as in self, or


• self as in feeling.

(13) He regards

• perception as self, or


• self as possessed of perception, or


• perception as in self, or


• self as in perception.

(14) He regards

• formations as self, or


• self as possessed of formations, or


• formations as in self, or


• self as in formations.

(15) He regards

• consciousness as self, or


• self as possessed of consciousness, or


• consciousness as in self, or


• self as in consciousness.

This is how, bhikshus, one is dragged along [distracted] by each present state as it arises.

And how, bhikshus, is one not dragged along [undistracted] by each present state as it arises?

(11) Here, bhikshus, a well-taught noble disciple, who has regard for the noble ones and is skilled and disciplined in their Dharma, who has regard for true persons and is skilled and disciplined in their Dharma,

does not regard

• form as self,


• nor self as possessed of form,


• nor form as in self,


• nor self as in form.

(12) He does not regard

• feeling as self,


• nor self as possessed of feeling,


• nor feeling as in self,


• nor self as in feeling.

(13) He does not regard

• perception as self,


• nor self as possessed of perception,


• nor perception as in self,


• nor self as in perception.

(14) He does not regard

• formations as self,


• nor self as possessed of formations,


• nor formations as in self,


• nor self as in formations.

Bhadd’eka,ratta Sutta

16 Doubts

He unwisely attends in this way:

(1) ‘Was I in the past?’

(2) ‘Was I not in the past?’

(3) ‘What was I in the past?’

(4) ‘How was I in the past?’

(5) ‘Having been what, did I become what in the past? [What was I before I became that in the past?]’

(6) ‘Will I be in the future?’

(7) ‘Am I not in the future?’

(8) ‘What will I be in the future?’

(9) ‘How will I be in the future?’

(10) ‘Having been what, will I become what in the future? [What now would lead me to that future
state?]’”

Or else, right now he inwardly has doubts about the present, thus:

(11) ‘Am I?’

(12) ‘Am I not?’

(13) ‘What am I?’

(10) ‘Having been what, what will I become in the future? [What now would lead me to that
future state?]’”

(11) ‘Am I?’

(12) ‘Am I not?’

(13) ‘What am I?’

(14) ‘How am I?’

(15) ‘Where has this being come from?’

(16) ‘Where will it [this being] go?’”

Sabb’āsava Sutta

I have quoted the Pali Suttas. I would believe the Āgama texts may have a similar parallel.

There are the 108 craving verbalization which will answer good householders question.

It's how ever good to relate ones actions as own and that there will be a fruit of them in the future, so the path is not one of "not mine" or "mine" extremes, but both used at proper time.

Much urged always: DON'T Waste your short lasting time of a seldom human and blessed existence!

Selves & Not-self: The Buddhist Teaching on Anatta is sure for good assistance and given for liberation.

(note that this Gift of Dhamma is not given for trade, stacks, exchange or entertainment, but for ones work trough maccharia to escape the wheel here and liberation)

yes to conceive (you in) the past or future or present is the opposite of the result and so opposite of the practice, as it is said in the suttanipata.

372. “A purified conqueror whose coverings are removed, a master of things, gone beyond, without impulse,
     skilled in the knowledge of the cessation of conditioned things, he
     would properly wander in the world. (14)


373. “One who has overcome mental constructs about things past and future, having overcome, wise about purity, released from all the
     sense bases, he would properly wander in the world. (15)


374. “Having known the state, having penetrated the Dhamma, having seen clearly the abandoning of the influxes, with the utter
     destruction of all acquisitions, 116 he would properly wander in the
     world.” (16)

it is not good to be ''Concerned, too, with the future or the past''

772. Stuck in the cave, densely covered over, dwelling immersed in bewilderment, [152] a person such as this is far from seclusion, for
     in the world sensual pleasures are not easily abandoned. (1)


773. Based upon desire, bound to enjoyment of existence, they let go with difficulty, for there is no release through others. Concerned,
     too, with the future or the past, they hanker for these sensual
     pleasures or earlier ones. (2)

again here

848. “How does he see, how does he behave, the one who is said to be ‘peaceful’? When asked by me, O Gotama, describe the supreme person.”
     (1)


849. “Devoid of craving before the breakup,” (said the Blessed One), “not dependent on the past, not to be reckoned in the middle, for him
     there are no preferences. (2) [167]


850. “He is without anger, unafraid, not boastful, not regretful, of speaking with reflection, not restless: he is truly a muni controlled
     in speech. (3)


851. “He is without attachment to the future; he does not sorrow over the past. As a seer of seclusion in the midst of contacts, he is not
     led astray among views. (4)

For minds able to practise the Noble Path, the Buddha taught when the past is recollected, it is to be recollected as merely 'aggregates' ('khandha'). In other words, the self-becomings or adherences ('nivasa') of the past must be seen as delusions or ignorance from the past. This is the 1st Knowledge for Enlightened. The Buddha taught:

At Savatthi. “Bhikkhus, those ascetics and brahmins who recollect
their manifold past abodes all recollect the five aggregates subject
to clinging or a certain one among them. What five?

“When recollecting thus, bhikkhus: ‘I had such form in the past,’ it
is just form that one recollects. When recollecting: ‘I had such a
feeling in the past,’ it is just feeling that one recollects. When
recollecting: ‘I had such a perception in the past,’ it is just
perception that one recollects. When recollecting: ‘I had such
volitional formations in the past,’ it is just volitional formations
that one recollects. When recollecting: ‘I had such consciousness in
the past,’ it is just consciousness that one recollects.

Therefore, bhikkhus, any kind of form whatsoever … Any kind of feeling
whatsoever … Any kind of perception whatsoever … Any kind of
volitional formations whatsoever … Any kind of consciousness
whatsoever, whether past, future, or present, internal or external,
gross or subtle, inferior or superior, far or near, all consciousness
should be seen as it really is with correct wisdom thus: ‘This is not
mine, this I am not, this is not my self.’

https://suttacentral.net/sn22.79/en/bodhi