How to represent the time series of the exchange price as a function (so that you can take the derivative)?

Question

Mathematics

There are values ​​of the price of an asset on the exchange. I want to represent a series as an approximate function so that I can differentiate it.
How is it properly done?
Or maybe you can immediately differentiate the time series in order to immediately take the derivative of the time series, or will it not work?
I will do it in python, there is a lot of data.
Good luck and achievements to all!

Answer 1

You have a discrete function. Accordingly, there will be a right-hand difference:
f'(t _i ) = (f(t _i+1 ) - f(t _i )) / (t _i+1 - t _i+1 )
or a left-hand difference:
f'(t _i ) = (f(t _i ) - f(t _i-1 )) / (t _i - t _i-1 )
You can also take the two-sided difference:
f'(t _i ) = (f(t _i+1 ) - f(t _i-1 )) / (t _i+1 - t _i-1 )