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:
- It easily handles structural breaks, shifts, time-varying parameters of some static model - just make those parameters dynamic states of a state-space model and model will automatically adjust to any shifts in parameters;
- It handles missing data very naturally, just do transition step of KF and don't do update step;
- It allows to change on-a-fly parameters of a state-space model itself (covariances of noises and transition/observation matrices) so if your current observation came from a little different source than others - you can easily incorporate it into estimation without doing anything special;
- Using above properties it allows easily handle irregular-spaced data: either change a model each time according to interval between observations or use regular interval and treat intervals without observations as missing data;
- It allows to use data from different sources simultaneously in the same model to estimate one underlying quantity;
- It allows to construct a model from several interpretable unobservable dynamic components and estimate them;
- Any ARIMA model can be represented in a state-space form, but only simple state-space models can be represented exactly in ARIMA form.