I I'm currently trying to extend a restricted ARMA(1,1) model into a state space model where extreme residuals (greater than a certain value) are allowed to have different effect on the state then non-extreme residuals.
The original model: y(t) = x(t) + error(t) x(t+1) = x(t) + δ * error(t) + u(t+1)
The extended model (e' being the extreme and e being non-extreme residuals): y(t) = x(t) + e(t) + e'(t) x(t+1) = x(t) + ϕ1 * e(t) + ϕ2 * e'(t) + v(t+1)
I understand that such non-smooth transformation will make the MLE considerably trickier, and my question is: am I able to customize sm.tsa.statespace.MLEModel to accommodate such model?
Thank you!