statsmodels.tsa.statespace.sarimax.SARIMAXResults.info_criteria¶

SARIMAXResults.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:

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

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):

$$\begin{array}{rl}AI{C}_L& =\log |Q|+\frac{2k}{n}\\ BI{C}_L& =\log |Q|+\frac{k\log n}{n}\\ HQI{C}_L& =\log |Q|+\frac{2k\log \log n}{n}\end{array}$$

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