Estimation with missing observations

i want to estimate a model for time t = 1 to t = T. Suppose one of the observables (lets call it x) that i want to use has data starting at t = 5. My question is can i still use x as an observable in bayesian estimation? can i do this in dynare? if yes, then how should i feed the data in dynare to tell it that this particular time series starts at a later date?

Dynare will use the Kalman filter to infer the value of the missing variables. See the description in the manual and the references therein. You don’t have to specify anything, you just have to enter the dataset with the missing observations left empty (in Excel) or with NaN (in Matlab).