We compare the forecasting performance of the generalized autoregressive conditional heteroscedasticity (GARCH) -type models with support vector regression (SVR) for futures contracts of selected energy commodities: Crude oil, natural gas, heating oil, gasoil and gasoline. The GARCH models are commonly used in volatility analysis, while SVR is one of machine learning methods, which have gained attention and interest in recent years. We show that the accuracy of volatility forecasts depends substantially on the applied proxy of volatility. Our study confirms that SVR with properly determined hyperparameters can lead to lower forecasting errors than the GARCH models when the squared daily return is used as the proxy of volatility in an evaluation. Meanwhile, if we apply the Parkinson estimator which is a more accurate approximation of volatility, the results usually favor the GARCH models. Moreover, it is difficult to choose the best model among the GARCH models for all analyzed commodities, however, forecasts based on the asymmetric GARCH models are often the most accurate. While, in the class of the SVR models, the results indicate the forecasting superiority of the SVR model with the linear kernel and 15 lags, which has the lowest mean square error (MSE) and mean absolute error (MAE) among the SVR models in 92% cases.

Research background: The Russian invasion on Ukraine of February 24, 2022 sharply raised the volatility in commodity and financial markets. This had the adverse effect on the accuracy of volatility forecasts. The scale of negative effects of war was, however, market-specific and some markets exhibited a strong tendency to return to usual levels in a short time. Purpose of the article: We study the volatility shocks caused by the war. Our focus is on the markets highly exposed to the effects of this conflict: the stock, currency, cryptocurrency, gold, wheat and crude oil markets. We evaluate the forecasting accuracy of volatility models during the first stage of the war and compare the scale of forecast deterioration among the examined markets. Our long-term purpose is to analyze the methods that have the potential to mitigate the effect of forecast deterioration under such circumstances. We concentrate on the methods designed to deal with outliers and periods of extreme volatility, but, so far, have not been investigated empirically under the conditions of war. Methods: We use the robust methods of estimation and a modified Range-GARCH model which is based on opening, low, high and closing prices. We compare them with the standard maximum likelihood method of the classic GARCH model. Moreover, we employ the MCS (Model Confidence Set) procedure to create the set of superior models. Findings & value added: Analyzing the market specificity, we identify both some common patterns and substantial differences among the markets, which is the first comparison of this type relating to the ongoing conflict. In particular, we discover the individual nature of the cryptocurrency markets, where the reaction to the outbreak of the war was very limited and the accuracy of forecasts remained at the similar level before and after the beginning of the war. Our long-term contribution are the findings about suitability of methods that have the potential to handle the extreme volatility but have not been examined empirically under the conditions of war. We reveal that the Range-GARCH model compares favorably with the standard volatility models, even when the latter are evaluated in a robust way. It gives valuable implication for the future research connected with military conflicts, showing that in such period gains from using more market information outweigh the benefits of using robust estimators.

Support vector regression is a promising method for time-series prediction, as it has good generalisability and an overall stable behaviour. Recent studies have shown that it can describe the dynamic characteristics of financial processes and make more accurate forecasts than other machine learning techniques. The first main contribution of this paper is to propose a methodology for dynamic modelling and forecasting covariance matrices based on support vector regression using the Cholesky decomposition. The procedure is applied to range-based covariance matrices of returns, which are estimated on the basis of low and high prices. Such prices are most often available with closing prices for many financial series and contain more information about volatility and relationships between returns. The methodology guarantees the positive definiteness of the forecasted covariance matrices and is flexible, as it can be applied to different dependence patterns. The second contribution of the paper is to show with an example of the exchange rates from the forex market that the covariance matrix forecasts calculated using the proposed approach are more accurate than the forecasts from the benchmark dynamic conditional correlation model. The advantage of the suggested procedure is higher during turbulent periods, i.e., when forecasting is the most difficult and accurate forecasts matter most.