statsmodels.tsa.statespace.kalman_smoother.SmootherResults smoothed_state definition

[Josh Spear]

Hi,

I understand the Kalman Smoother implements the algorithm from Durbin and Koopman 2012. Please can I confirm whether the output of the  smoothed_state is the Expected value of the state (alpha) given the observations (y)  or whether it is the smoothed realisations of the state?

Many thanks, 

Josh 

[Chad Fulton]

Hi Josh,

Yes, `smoothed_state` it is the expected value of the state vector conditional on the entire dataset. It's what Durbin and Koopman denote by \hat \alpha.

Samples from the joint distribution of the state vector conditional on the entire dataset can be drawn by creating a simulation smoother object, running the `simulate` method, and then accessing the `simulated_state` attribute.

Best,

Chad

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[Josh Spear]

Hi Chad, 

Ah perfect thank you. Just to confirm, so the simulated_state attribute from the simulate method will be equivalent to \tilda \alpha in D&K 2012?

Thanks again for your help.

Josh

[Chad Fulton]

Hi Josh,

Yes, that is correct, `simulated_state` is \tilde \alpha.

In case it's useful, an example notebook that uses simulation smoothing can be found at https://www.statsmodels.org/devel/examples/notebooks/generated/statespace_tvpvar_mcmc_cfa.html

Best,

Chad

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[Josh Spear]

Thank you Chad!