Financial time series prediction is a challenging task due to the noisy, non-stationary and chaotic nature series. Traditional methods, especially autoregressive integrated moving average (ARIMA) has a wide range of application. With the rapid development of information technologies in the last two decades, various deep learning methods which are inspired by human brain that consists of inter-connected neurons have been proposed in order to improve the prediction performance of time series. As the data amount increases, these methods have been seen as an alternative for traditional ones having some important limitations. The main purpose of this study is to determine whether the deep learning methods outperform than traditional ARIMA method in predicting the BIST 30, BIST 50 and BIST 100 price indices. The prediction performance of ARIMA is compared against the prediction performances of Long Short-Term Memory and Gated-Recurrent Unit for each BIST price index. According to the root mean square evaluation metric, it is found that ARIMA models have better performance in predicting BIST 30, BIST 50 and BIST 100 indices than deep learning architectures.