Forecasting Financial Returns Volatility: A GARCH-SVR Model

Support vector regression (SVR) is a semiparametric estimation method that has been used extensively in the forecasting of financial time series volatility. In this paper, we seek to design a two-stage forecasting volatility method by combining SVR and the GARCH model (GARCH-SVR) instead of replacing the maximum likelihood estimation with the SVR estimation method to estimate the GARCH parameters (SVR-GARCH). To investigate the effect of innovations in different distributions, we propose the GARCH-SVR and GARCH-t-SVR models based on the standardized normal distribution and the standardized Student's t distribution, respectively. To allow asymmetric volatility effects, we also consider the GJR-(t)-SVR models. The forecast performance of the GARCH-(t)-SVR and GJR-(t)-SVR models is evaluated using the daily closing price of the S&P 500 index and the daily exchange rate of the British pound against the US dollar. The empirical results obtained for one-period-ahead forecasts suggest that the GARCH-(t)-SVR models and GJR-(t)-SVR models improve the volatility forecasting ability.