In this article, we consider two competing models, viz., ARMA with conditional heteroscedasticity and GARCH-M models. Both the models capture inherent linear autocorrelation structure in the data. These two models are non-nested in nature. No one is a particular case of other model. Applied researchers are generally tempted to build an appropriate ARMA model based on Box-Jenkins’s methodology, namely based on ACF and PACFs overlooking the existence of other competing models. In this paper, the usual AIC/BIC criteria are used to identify the appropriate model. The detailed simulation study shows that the AIC/BIC can indeed select the true model.