My data set is quarterly time seires data (around 140 data points).
Method 1: simple OLS regression with 5-6 exogenous variables, which are drivers of the dependent variable. None of the explanatory variables are lagged, AR or MA.
Method 2: ARIMA model using maximum likelihood with the same exogenous variables. AR, MA, or differencing are based on residual plots. I chose differencing with the same quarter of the prior year and AR of the same quarter of the prior year.
AIC or BIC from OLS regression are around 200 but from ARIMA are around 900. I have tried various ARIMA models by testing different p,q,d but AIC is still higher than OLS's.
Is it reasonable to select models between OLS regression and ARIMA for time series data based on AIC or BIC? What criterion should be used?
Amy comments would be appreciated.