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This research investigates whether the US stock volatility index (S&amp;P 500 index) has the forecasting ability to predict the volatility of CAC index (France), DAX index (Germany), and FTSE index (the UK) by employing a multivariate heterogeneous autoregressive realized volatility jump (MHAR-RV-CJ) model. Our empirical results provide consolidated comparisons using univariate and multivariate models. The in-sample results show us the US volatility will improve the long-term volatility regression coefficient. Moreover, our proposed model, the MHAR-RV-CJ model, nearly surpasses all competing models at out-of-sample forecasting, indicating that considering the multivariate DCC-GARCH information between US-France, US-Germany, and US-UK stock markets and jump component structures can help to predict individual European stock market volatility. Unsurprisingly, several forecasting evaluation tests and further analysis (high/low volatility) confirm the robustness of our results.

Does the US stock market information matter for European equity market volatility: a multivariate perspective?