Determination of the lag length of an autoregressive process is one of the most difficult parts of ARIMA modeling. Various lag length selection criteria (Akaike Information Criterion, Schwarz Information Criterion, Hannan-Quinn Criterion, Final Prediction Error, Corrected version of AIC) have been proposed in the literature to overcome this difficulty. We have compared these criteria for lag length selection for three different cases that is under normal errors, under non-normal errors and under structural break by using Monte Carlo simulation. It has been found that SIC is the best for large samples and no criteria is not useful for selecting true lag length in presence of regime shifts or shocks to the system. It is the first ever study where lag length under the presence of structural breaks have also been made in order to see that if without employing structural stability tests what could be the impact on lag length selection criteria by these methods.