Which AIC value to use from R's sarima() function for model comparison I'm using R's 'astsa' package and I get the following output from sarima. 
Which AIC value would I use to compare this model (let's call it A) against others? When trying another model (B), model A's fit$AIC (858.19) is greater than model B's, but model A's AIC (12.38841) is less than model B's, so I'm not sure which model to choose.
What's the difference between the two AIC's, AICc's, and BIC's? I've checked the sites below, among others, but haven't been able to figure it out. Any help is much appreciated.
http://stat.ethz.ch/R-manual/R-patched/library/stats/html/arima.html
http://www.inside-r.org/packages/cran/astsa/docs/sarima
$fit
Series: xdata 
ARIMA(0,1,1)(1,1,1)[12]                    

Coefficients:
         ma1    sar1     sma1
     -0.3282  0.5529  -0.8835
s.e.   0.3290  0.4751   0.8635

sigma^2 estimated as 82513:  log likelihood=-425.1
AIC=858.19   AICc=858.93   BIC=866.5

$AIC
[1] 12.38841

$AICc
[1] 12.42448

$BIC
[1] 11.48327

 A: Akaike's Information Criterion (AIC): Formally, AIC is defined as $2 \log L_k+ 2k$ where $L_k$ is the maximized log likelihood and $k$ is the number of parameters in the model. For the normal regression problem, AIC is an estimate
of the Kullback-Leibler discrepancy between a true model and a candidate model.
AIC, Bias Corrected (AICc): A corrected form, suggested by Sugiura (1978), and expanded by Hurvich and Tsai (1989), can be based on small-sample distributional results for the linear regression model
Bayesian Information Criterion (BIC): is also called the Schwarz Information Criterion (SIC), for an approach yielding the same statistic based on a minimum
description length argument. Various simulation studies have tended to verify that BIC does well at getting the correct order in large samples, whereas
AICc tends to be superior in smaller samples where the relative number of
parameters is large.
Example:
sarima(gnpgr, 1, 0, 0) # AR(1)
$AIC: -8.294403 $AICc: -8.284898 $BIC: -9.263748

sarima(gnpgr, 0, 0, 2) # MA(2)
$AIC: -8.297693 $AICc: -8.287854 $BIC: -9.251711

The AIC and AICc both prefer the MA(2) fit, whereas the BIC prefers the
simpler AR(1) model. It is often the case that the BIC will select a model
of smaller order than the AIC or AICc. It would not be unreasonable in this
case to retain the AR(1) because pure autoregressive models are easier to
work with.
A: The first AIC from the sarima command comes from the formal definition of AIC, the second version comes from a reduced form, which is only applicable in the context of normal regression, see:
https://en.wikipedia.org/wiki/Akaike_information_criterion#Comparison_with_least_squares
