I am interested in the parameter estimation problem described as follows:

Given a dataset of observations: Y1, Y2,..., Yn and a nonlinear discrete-time model:

y(n+1) = F(y(n), theta), y(1) = Y1, n > 0,

where theta is a vector of real parameters.

My question is: How we can determine the optimal parameter vector theta to ensure that the discrete-time model best fits to the data?

Thank you so much for your time and consideration!