Modelling Di erent Volatility Components in High-Frequency Financial Returns

This paper considers simultaneous modelling of seasonality, slowly changing unconditional variance and conditional heteroskedasticity in high-frequency nancial returns. A new approach, called a seasonal SEMIGARCH model, is proposed to perform this by introducing multiplicative seasonal and trend components into the GARCH model. A data-driven semiparametric algorithm is developed for estimating the model. Asymptotic properties of the proposed estimators are investigated brie y. An approximate signi cance test of seasonality and the use of Monte Carlo con dence bounds for the trend are proposed. Practical performance of the proposal is investigated in detail using some German stock price returns. The approach proposed here provides a useful semiparametric extension of the GARCH model.