/Statsmodels

# statsmodels.tsa.statespace.structural.UnobservedComponentsResults.info_criteria

UnobservedComponentsResults.info_criteria(criteria, method='standard')

Information criteria

Parameters: criteria ({'aic', 'bic', 'hqic'}) – The information criteria to compute. method ({'standard', 'lutkepohl'}) – The method for information criteria computation. Default is ‘standard’ method; ‘lutkepohl’ computes the information criteria as in Lütkepohl (2007). See Notes for formulas.

#### Notes

The ‘standard’ formulas are:

$\begin{split}AIC & = -2 \log L(Y_n | \hat \psi) + 2 k \\ BIC & = -2 \log L(Y_n | \hat \psi) + k \log n \\ HQIC & = -2 \log L(Y_n | \hat \psi) + 2 k \log \log n \\\end{split}$

where $$\hat \psi$$ are the maximum likelihood estimates of the parameters, $$n$$ is the number of observations, and k is the number of estimated parameters.

Note that the ‘standard’ formulas are returned from the aic, bic, and hqic results attributes.

The ‘lutkepohl’ formuals are (Lütkepohl, 2010):

$\begin{split}AIC_L & = \log | Q | + \frac{2 k}{n} \\ BIC_L & = \log | Q | + \frac{k \log n}{n} \\ HQIC_L & = \log | Q | + \frac{2 k \log \log n}{n} \\\end{split}$

where $$Q$$ is the state covariance matrix. Note that the Lütkepohl definitions do not apply to all state space models, and should be used with care outside of SARIMAX and VARMAX models.

#### References

 [*] Lütkepohl, Helmut. 2007. New Introduction to Multiple Time Series Analysis. Berlin: Springer.