The study is aimed at identifying the orders of Time Series Models in Non-Stationarity Non-normal data structure from Uniform distributions with a view to determining the best Autoregressive/ Moving Average orders from time series models (ARMA and ARIMA) under different underline distributions when Non-Stationarity assumption is assumed. The data is generated from Autoregressive (AR) linear of second orders of general classes of Autoregressive functions. The generation of the data used for this simulation study is non-stationary cases and nonnormal. The data were simulated for both response variables and error terms from non-normal Distribution. The result shows that the values of the penalty function: AIC, BIC, HQIC and FPE of the order selection increases with increase in sample size but decreases with increasing order. It was observed that at both lower (20, 40) and larger (160,180 and 200) sample sizes, models with smallest orders. Similarly, the selection process is tied to the principle of parsimony i.e smaller orders are selected, but vary with the variation in the distribution of the series. The study recommends the need to develop a methodology for model selection combining objective and subjective techniques.