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Given all good properties of state-space models and KF, I wonder - what are disadvantages of state-space modelling and using Kalman Filter (or EKF, UKF or particle filter) for estimation? Over let's say conventional methodologies like ARIMA, VAR or ad-hoc/heuristic methods.

Are they hard to calibrate? Are they complicated and hard to see how a change in a model's structure will affect predictions?

Or, put another way - what are advantages of conventional ARIMA, VAR over state-space models?

I can think only of advantages of a state-space model: