I would like to perform something that resembles a curve fitting optimization but for which i could not find much info.
Lets say i have a function that yields a time series. What i would like to do is tune the parameters of this function so that the time series it yields has a specific shape. For instance i want it to output a step, or two steps back to back. What i don't know (or care about for that matter) is the height of the steps.
For a single step, a naive solution would be to simply take the average of the output and compute the RMSE of the output to it's average and minimizing it.
However this gets more and more complicated for more complex shapes (the two steps example is already a pain with this method)
Would there be a mathematical tool that would facilitate this?