Vector autoregression - number of variables to use

Question

When building a vector autoregression model is there some theory that would guide me in chosing the number of variable to include? For example, I have about 3000 data points and I would like to get an idea of how many lags of explanatory variables to ues.

Answer 1

The standard practice is to use some sort of information criterion, usually the Akaike Infromation Criterion (AIC) or the Schwarz Information Criterion (SIC).

The AIC is defined as 2k-log(L), where k is the number of parameters, and L is the maximized likelihood function of the model (estimated with k parameters).

The SIC is defined as k*log(n)-log(L), where k and L are as above, and n is the number of observations of the model.

In general, one adopts the model that minimizes the chosen criterion.