I recently started to deepen my knowledge about interest rates' modelling, and I am trying to estimate a two-factor Ornstein–Uhlenbeck process using Euro area OIS rates by means of an Iterated extended Kalman filter with Maximum Likelihood estimation.
Without entering into the details of the model, I have a conceptual doubt regarding the Extended Kalman filter. From what I understood, given a set of initial parameters' estimates (some initial guesses), the filter allows us to improve those estimates, giving us a final set of estimated parameters (according to some tolerance we may specify).
My question is quite simple: if I use the final set of parameters I obtain from a first estimation of the model as initial guesses for a second estimation of the model, that is I repeat the estimation of my model using as initial parameters the final ones previously estimated, should I expect to find a (new) final parameters set that is very similar, if not equal, to the initial one?
I am asking this because my algorithm provides me with substantially different estimates and I am trying to figure out why.
Probably this may sound a bit silly to most of you, but as I mentioned before I am quite new in this area and I am trying to grasp some fundamental concepts.
Thank you!