Owing to their ability to capture complex non-linear patterns and to memorize long-term dependencies, LSTM and GRU models are widely used to forecast time series. However, stock price data presents another layer of complexity due to their volatility. In this paper, a comparative study between LSTM and GRU is held using Hyperband (HB) as the Hyperparameter Optimization (HPO) technique for 4 different-sized datasets of stock prices of retail supply chains. The paper aims to provide an intuition about the accessibility and the performance of Automated Machine Learning (AutoML) methods in tuning powerful Deep Learning (DL) models such as LSTM and GRU. To this end, a basic forecasting framework is provided to outline the tuning steps of different hyperparameters. After model building, the performance evaluation using RMSE, MAE, RMSPE, MAPE and R2 leads to a discussion of the models’ accuracy in validation and test sets. Finally, an overall conclusion paves the way for the main improvements to implement as well as perspectives for future work.