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How o treat time when using stocks and a growth model (longitudinal data)

Hello,

I have been studying multilevel models to understand how I can use it to
investigate the behavior of stocks listed on a exchange. I am still very
new with this methodology so I would like to ask if its possible to do that
using growth model and how I should treat stocks that start to be traded in
different period (for instance, stock of company A is traded since 1998 and
stock of company B is traded since 2005).

Thank you for any help.