Volatility modeling on high-frequency data

This master thesis deals with volatility modeling on high-frequency data. There are four types of HAR models applied: HAR-RV, HAR-RV-J, HAR-Q and HAR-Q-J. The analysis is carried out on a 5-minute time series of the Moscow Stock Exchange Index (MOEX). The main aim of the thesis is to select the best model for modeling and forecasting volatility in financial markets. Another goal of the thesis is to find out if the extension of basic types of HAR models by realized quarticity and by jump variables has a positive effect on the predictive capabilities of models. Volatility will be estimated for the next day and the following week. In the application part of this thesis, the predictive capability of HAR models will be compared using RMSE, determination index and Mincer - Zarnowitz regression on both in-sample and out-sample data. The results of the analysis show that the extension of HAR models by jump variables does improve the volatility forecasts for the following day, but the extension by realized quarticity does not have positive impact to the performance of model. In the case of volatility predictions for the following week, it cannot be unambiguously determined if the realized quarticity improves predictive ability of HAR models. If models are extended by jump variables, we can see an increase in the performance of the models in volatility prediction for the following week. The HAR-RV-J model achieved the best results at the daily forecast horizon. Also, at the weekly forecast horizon, the best model is HAR-RV-J.