In financial time series modelling and forecasting, combining ARMA and GARCH models tend to produce superior and reliable models for volatility persistence, half-life volatility and backtesting (application of model in real life). In Nigeria, banking stocks are mostly traded because of its potential benefits to investors. This study modelled and forecasted the Guaranty Trust (GT) Bank daily stock returns from January 2nd 2001 to May 8th 2017 data set collected from a secondary source. The ARMA-GARCH models, persistence, half-life and backtesting were used to analysed the collected data using student t and skewed student t distributions, and the analyses are carried out R environment using rugard and performanceAnaytics Packages. The study revealed that using the lowest information criteria values only could be misleading rather we added the use of backtesing. The ARMA(1,1)-GARCH(1,1) models fitted exhibited high persistency in the daily stock returns while the days it takes for mean-reverting of the models ranges from 5 days to 100 days but unfortunately the models failed backtesting. The results further revealed ARMA(1,1)-eGARCH (2,2) model with student t distribution provides a suitable model for evaluating the GT bank stock returns among the competing models while it takes less than 30 days for the persistence volatility to return back to its average value of the stock returns. This study recommended that researchers should adopt backtesting approach while fitting GARCH models while GT bank stocks investor should be assured that no matter the fluctuations in the stock market, the GT bank stock returns has the ability to returns to its mean price return.