Suppose I have x and y variables and their measurements over time t.
If y=f(t)x+g(t)
How can I find the functional forms of the f(t) and g(t)? In some sense this a linear regression with time varying slope and baseline but i am unablemto come up with a functional form for them. Are they any way to at least approximate their functional forms?
I have tried decompose polynomial functions for for g(t) and f(t) but had to increase the polynomial order and got ill conditioned results.
