I am currently estimating the parameters of an interest rate model by means of a maximum likelihood estimation in combination with the iterated extended Kalman filter, and I obtain incredibly low values of standard errors.
Such estimation technique requires the use of "initial guesses" of the parameters to be estimated and, for some reasons which are not relevant to this question, I am using as initial guesses the estimates obtained from another estimation of the model.
Given the fact that the estimated parameters by means of the maximum likelihood estimation in combination with the iterated extended Kalman filter turn out to be equivalent to their corresponding initial guesses, I am wondering if such low standard errors can be explained by such results.
In other words: is it possible that by addressing the estimation with initial guesses that are already the "correct" values of the parameters lead to such a high level of accurateness?
Many thanks to whoever will help me!