Solved – What are disadvantages of state-space models and Kalman Filter for time-series modelling

arimakalman filtertime seriesvector-autoregression

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:

  1. 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;
  2. It handles missing data very naturally, just do transition step of KF and don't do update step;
  3. 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;
  4. 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;
  5. It allows to use data from different sources simultaneously in the same model to estimate one underlying quantity;
  6. It allows to construct a model from several interpretable unobservable dynamic components and estimate them;
  7. Any ARIMA model can be represented in a state-space form, but only simple state-space models can be represented exactly in ARIMA form.

Best Answer

Here is some preliminary list of disadvantages I was able to extract from your comments. Criticism and additions are very welcome!

Overall - compared to ARIMA, state-space models allow you to model more complex processes, have interpretable structure and easily handle data irregularities; but for this you pay with increased complexity of a model, harder calibration, less community knowledge.

  1. ARIMA is a universal approximator - you don't care what is the true model behind your data and you use universal ARIMA diagnostic and fitting tools to approximate this model. It is like a polynomial curve fitting - you don't care what is the true function, you always can approximate it with a polynomial of some degree.
  2. State-space models naturally require you to write-down some reasonable model for your process (which is good - you use your prior knowledge of your process to improve estimates). Of course, if you don't have any idea of your process, you always can use some universal state-space model also - e.g. represent ARIMA in a state-space form. But then ARIMA in its original form has more parsimonious formulation - without introducing unnecessary hidden states.
  3. Because there is such a great variety of state-space models formulations (much richer than class of ARIMA models), behavior of all these potential models is not well studied and if the model you formulated is complicated - it's hard to say how it will behave under different circumstances. Of course, if your state-space model is simple or composed of interpretable components, there is no such problem. But ARIMA is always the same well studied ARIMA so it should be easier to anticipate its behavior even if you use it to approximate some complex process.
  4. Because state-space allows you directly and exactly model complex/nonlinear models, then for these complex/nonlinear models you may have problems with stability of filtering/prediction (EKF/UKF divergence, particle filter degradation). You may also have problems with calibrating complicated-model's parameters - it's a computationally-hard optimization problem. ARIMA is simple, has less parameters (1 noise source instead of 2 noise sources, no hidden variables) so its calibration is simpler.
  5. For state-space there is less community knowledge and software in statistical community than for ARIMA.
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