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In volatility forecasting literature, Markov switching multifractal (MSM) models are well known for capturing many important stylized facts such as long memory and fat tails. MSM delivers stronger performance both in- and out-of-sample than GARCH-type models in long-term forecasts. However, the literature shows that MSM forecasts only slightly improve on GARCH(1,1) at short-term intervals. This indicates that there may exist certain patterns to be discovered in the innovation part. To enhance MSM's prediction accuracy at the short-term level with higher frequency data, a hybrid model of the MSM model and support vector regression (SVR) is proposed, in which a particle swarm optimization (PSO) algorithm is applied to optimize hyperparameters of the support vector regression in the scope of constraint permission. The method is referred to as MSM-PSO-SVR. Further, we introduce the Fourier kernel MSM-PSO-SVR and evaluate the performance of various MSM-PSO-SVR models in terms of mean absolute error (MAE) and the mean squared error (MSE) with one-minute data of the exchange traded fund (ETF) SPDR S&amp;P 500 Trust ETF (ticker symbol: SPY). The experimental results show that the proposed approach outperforms the other competing peer models and in particular, the selection of SVR kernel might yield significant boosts in forecasting ability. Results of Hansen's Superior Predictive Ability test further validate the conclusion.

Short-term volatility forecasting with kernel support vector regression and Markov switching multifractal model