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stage of the BJ method and is the main issue to be 
dealt with when analyzing shorter time series. 
AIC approach To circumvent the subjectivity of the 
identification of the model with the BJ method and 
to aid in the determination of the final orders of the 
ARMA processes a wide variety of model selection 
criteria have been developed (De Gooijer et ah, 1985). 
The most frequently used are the Akaike information 
criteria (AIC) (Akaike, 1974) and the small-sample, 
bias-corrected equivalent, AIC c (Hurvich and Tsai, 
1989). Contrary to the Box- Jenkins method, AIC/AIC c 
selection of a model involves the a priori estimation by 
maximum likelihood methods of a set of model struc- 
tures (here termed the candidate set). This estimation 
is followed by the determination of the AIC/AIC c values 
for each individual model. The model with minimum 
AIC/AIC c is then selected as the model that is closest 
to the statistical process “generating” the data. In 
SARIMA models, AIC is calculated as 
AIC = -21n(L)+2r , 
where ln(L) is the log-likelihood of the model, r=p+ 
q+P+Q+1, and the AIC c , is given by 
AIC c =-21n(L)+2r-t-2r(r+l)/(tt-r-l) , 
where n=N-DS-d is the number observations used to 
fit the model. AIC/AIC c constitute objective methods to 
achieve model parsimony through a trade-off between 
the variance explained by the model and penalty terms 
caused by excessive model parameters. Both of them are 
well founded in the principles of information and likeli- 
hood theory and have been applied extensively in time 
series, fisheries, and ecological literature (e.g., Brock- 
well and Davis, 2002; Burnham and Anderson, 2002; 
Hanson et al., 2006). Burnham and Anderson (2002) 
suggest AIC c is used when n/r <40, which prompts the 
consideration of this small-sample, bias-corrected ver- 
sion of AIC in studies of short time series. 
