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.