This paper examines the out-of-sample accuracy of recurrent artificial neural networks (ANNs) compared to traditional econometric models for the prediction of realized volatility. We focus on a horserace between the heterogeneous autoregressive (HAR) model, its Markov-switching extension (MS-HAR), multi-layer perceptrons (MLP), and long short-term memory (LSTM) networks across 31 international equity indices. Using high-frequency realized volatility data, we evaluate predictive performance based on four loss functions and test for equal accuracy using Diebold-Mariano tests. Our results suggest that the HAR and MS-HAR models often deliver the most accurate forecasts, outperforming LSTMs. However, differences in out-of-sample accuracy between LSTM, HAR, and MS-HAR models are not always statistically significant. We conclude that ANNs do not consistently outperform HAR-based models in equity volatility forecasting.