# How is the Akaike Information Criteron applied for model with large number of predictors?

I am reading a paper (details not very relevant) which assumes that the market cost $C$ of a trade is related to $N$ predictors $X_1,\dots,X_N$ (page 25) through a linear relationship

$$C = \beta_0 + \beta^TX_{1:N}$$

where the number of predictors $N=30$. The paper makes the following claim (page 29)

We estimate the linear regression model using ordinary least squares. We apply the Akaike criterion to delete any redundant explanatory variables from the regression model.

I am familiar with AIC as a method for model selection, but here there are 30 different variables and $2^{30}$ possible models. How did the authors use the AIC to determine which explanatory variables were 'redundant'?

From that methods description (I also looked briefly at the paper) I don't think it is possible to say exactly what they did, so the methods are very poorly written. I could imagine that their "final model" is an AIC- weighed model (maybe using an unknown $\Delta AIC$ cutoff) or it is simply the model that minimize AIC, but maybe you already guessed as much. Either way, it would have been just as easy to say exactly what they did, and to simply state that they deleted "redundant" variables is very unclear. It might be that the "Akaike criterion" is interpreted as something specific within the economics/trade-modelling field (I wouldn't know), but I would then have expected a citation after the statement.