statsmodels.tsa.statespace.mlemodel.MLEResults.info_criteria

MLEResults.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’ formulas 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.