Machine Learning, Neural Networks and Econometric Models for Prediction the Realized Volatility of Bitcoin and E-Mini S&P500

The article compares ARMA, boosting, neural network models, GARCH and HAR models, and proposes a new efficient method for forecasting one day ahead of the realized volatility of financial series. The GARCH and HAR models are taken as comparable models, which showed the best results in Manevich et al. (2023). In addition, the transfer learning phenomenon for boosting and neural network models is investigated. Bitcoin and E-mini S&P 500 are chosen as examples. Realized volatility is calculated from intraday (intraday - 24 hours) data. The calculation is based on the closing values of the internal five-minute intervals. All days of the week are almost equally present among the days selected for forecasting. The comparison is made on the observation interval from 01.01.2018 to 29.12.2021. Since there could be (and have been) structural changes in the markets during this interval, the models are evaluated in sliding windows of 399 days length. For each time series, we compare three-parameter enumeration boostings, about 10 different neural network architectures, ARMA models, a newly designed method, and different transfer learning and training sample expansion options. It is shown that GARCH and HAR models are inferior to other listed methods and models. CNN architecture is the most suitable for financial time series forecasting. The proposed method shows the results comparable to neural networks and boostings in precision. Transfer learning shows improvement in some cases, especially for neural networks, and needs to be studied in more detail. ARMA models outperform other listed methods in some cases. The smallest relative errors for the Bitcoin and E-mini S&P 500 realized volatility predictions are 25.28% and 30.74%, respectively