Využití Hidden Markov Modelů při predikci finančních časových řad

This thesis is concerned with the application of Hidden Markov Models (HMM) for financial time series prediction, particularly realized volatilities. The aims of this thesis are to test the predictive accuracy of models based on HMM and to investigate the dependencies in a time series of realized volatilities. The predictive power of the models is tested on predictive horizons of 1-, 5- and 20-day over a period of 100 days. The HMM based models are compared to GARCH benchmark models for predicting volatilities. Daily realized data from the Oxford-Man Institute of Quantitative Finance are used consisting of 22 time series of tradable indices from 2000 to 2020. The dependencies in the time series of realized volatilities are examined using the Hurst exponent and the Hall-Wood Fractal Dimension. The first predictive model is based on Hassan's approach where sequences from historical data with similar likelihood values are the key for predicting the future values. The second model is the Markov-Switching Multifractal Model (MSMM). The results obtained using the Hurst exponent and the fractal dimension imply that the realized volatility time series are rougher than classic Brownian motion and have some dependencies within. The predictive power of the HMM based models are encouraging and in some cases offer a preferable alternative to GARCH models.