[SOLVED] How to generate a state space model from data?

How to generate a state space model from data?

I am trying to identify a state space model from discrete time series data in Python using statsmodels library: statsmodel.tsa.statespace.sarimax.SARIMAX.

I need the matrices of the state space general form (here the statsmodel reference): from the statsmodel page these matrices are explained but it is not clear how to extrapolate them.

For example if I want to apply a kalman filter to the identified model (by means of a sarimax) I need the matrices described in this picture state space matrices needed

Is it possible to obtain the matrices coefficients with statsmodel?

Solution

All of the state space system matrices are saved in the filter_results attribute of the fitted model. The names of the matrices are given in the links that you included in your answer (e.g. "design", etc.)

For example:

model = SARIMAX(Y_tr, exog = X_tr, order = (p,d,q), enforce_invertibility = False)
best_model = model.fit()

print(best_model.filter_results.design)
print(best_model.filter_results.obs_cov)
# ...