I'm new here and wondering if anyone could give me some hints on how to estimate the time varying coefficient and state variable together. Here is my model:
observation equation: $Y(t)= A(t)X(t)+ w(t)$,
state equation: $X(t)=\phi X(t-1)+v(t)$,
here I have time varying coefficient $A(t)$, it doesn't depend on any predetermined parameter $\theta$, for example. If I treat $A(t)$ as another state variable, then it is nonlinear state space, I have no idea how to estimate multiplicative state variables. Any hints? Thank you.