Comparison of Cryptocurrency and Stock Market Volatility Forecast Models

The article compares GARÑH and HAR models for 1 day ahead forecasting performance of the realized volatility of financial series. As an example, the cryptocurrency with the largest capitalization, Bitcoin, was chosen. Its realized volatility is calculated from intraday (24 hours) data, using the closing values of five-minute trading intervals. The paper proposes a method for calculating realized volatility for the case of gaps in 5-minute intraday data. This makes it possible to achieve comparability of the daily values of the realized volatility of assets with different trading times. All days of the week are almost equally present among the days selected for forecasting. For comparison, a stock market asset was chosen, E-mini S&P 500, a futures contract that is traded 23 hours a day. We use data from 01/01/2018 to 12/29/2021. Since there could be (and were) structural changes in the markets in this interval, the models are evalua­ted in rolling windows 399 days long. For each series 810 GARCH models and 46312 HAR models are compared. The MCS test is used to select the best models (at the significance level of 0,01). It is shown that GARCH models are inferior to HAR models in the accuracy of forecasting both the realized volatility of Bitcoin and the E-mini S&P 500. At the same time, the relative accuracy of the forecast of the realized volatility of Bitcoin is higher than the accuracy of the forecast of the realized volatility of the E-mini S&P 500 futures. The smallest relative errors for Bitcoin and E-mini S&P 500 realized volatility forecasts are 29,51% and 36,12%, respectively.