In financial research papers, I have seen several times that the lag length in an ARMA model has been determined using BIC. Do the researchers estimate the lag length before considering other variables?
Would you compare the BIC values of the just the dependent variable and its lags or would you compare the BIC of the full model with the other exogenous variables.
Should I use method 1)
BIC1 Y(t) = c + Y(t-1)
BIC2 Y(t) = c + Y(t-1) + Y(t-2)
or should I use method 2)
BIC1 Y(t) = c + Y(t-1) + x1 + x2 + x3
BIC2 Y(t) = c + Y(t-1) + Y(t-2) + x1 + x2 + x3