Information criteria

To assess model adequacy, `aicbic`

computes information criteria given loglikelihood values obtained by fitting competing models to data.

In small samples, AIC tends to overfit. To address overfitting, AICc adds a size-dependent correction term that increases the penalty on the number of parameters. AICc approaches AIC asymptotically. The analysis in [3] suggests using AICc when

`numObs/numParam`

<`40`

.When econometricians compare models with different numbers of autoregressive lags or different orders of differencing, they often scale information criteria by the number of observations [5]. To scale information criteria, set

`numObs`

to the effective sample size of each estimate, and set`'Normalize'`

to true.

[1] Akaike, Hirotugu. "Information Theory and an Extension of the Maximum Likelihood Principle.” In *Selected Papers of Hirotugu Akaike*, edited by Emanuel Parzen, Kunio Tanabe, and Genshiro Kitagawa, 199–213. New York: Springer, 1998. https://doi.org/10.1007/978-1-4612-1694-0_15.

[2] Akaike, Hirotugu. “A New Look at the Statistical Model Identification.” *IEEE Transactions on Automatic Control* 19, no. 6 (December 1974): 716–23. https://doi.org/10.1109/TAC.1974.1100705.

[3] Burnham, Kenneth P., and David R. Anderson. *Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach*. 2nd ed, New York: Springer, 2002.

[4] Hannan, Edward J., and Barry G. Quinn. “The Determination of the Order of an Autoregression.” *Journal of the Royal Statistical Society: Series B (Methodological)* 41, no. 2 (January 1979): 190–95. https://doi.org/10.1111/j.2517-6161.1979.tb01072.x.

[5] Lütkepohl, Helmut, and Markus Krätzig, editors. *Applied Time Series Econometrics*. 1st ed. Cambridge University Press, 2004. https://doi.org/10.1017/CBO9780511606885.

[6] Schwarz, Gideon. “Estimating the Dimension of a Model.” *The Annals of Statistics* 6, no. 2 (March 1978): 461–64. https://doi.org/10.1214/aos/1176344136.