Comment: 51 pages, 16 figure, 18 tablesThe Stochastic Volatility (SV) model and its variants are widely used in the financial sector while recurrent neural network (RNN) models are successfully used in many large-scale industrial applications of Deep Learning. Our article combines these two methods in a non-trivial way and proposes a model, which we call the Statistical Recurrent Stochastic Volatility (SR-SV) model, to capture the dynamics of stochastic volatility. The proposed model is able to capture complex volatility effects (e.g., non-linearity and long-memory auto-dependence) overlooked by the conventional SV models, is statistically interpretable and has an impressive out-of-sample forecast performance. These properties are carefully discussed and illustrated through extensive simulation studies and applications to five international stock index datasets: The German stock index DAX30, the Hong Kong stock index HSI50, the France market index CAC40, the US stock market index SP500 and the Canada market index TSX250. An user-friendly software package together with the examples reported in the paper are available at \url{https://github.com/vbayeslab}.