ABSTRACT The study aimed to identify the orders of GARCH Models in Non-Stationarity and Non-normal data structure. Data were simulated that satisfied the non-stationary and non-normal requirement. The study fitted several GARCH models with the orders (1,1), (1,2), (2,1) and (2,2) on the simulated data at sample sizes 20, 40, 60, 80, 100, 120, 140, 160, 180 and 200 respectively. The penalty functions of AIC, BIC, SIC and HQIC used in assessing the best fit model. It was observed that parsimonious models were selected as the best fit in most of the scenario. GARCH model order selection is insensitive to the distribution which the time series conforms. Models fitted and selected for different conditions of non-Stationarity and non-normal data structure were tested on real life data with similar conditions and the selection proved to be appropriate in identifying the orders in relation to the conditions of the series. The study recommends that for every time series model order selection tests for normality and otherwise should be of priority just as that of Stationarity. Keywords: Forecasting; GARCH model; Non-Stationary Data; Non-Normal Data Structure